A universal mercy
The birth of the Prophet (peace and blessings be upon him) is a divine mercy in the history of man. The Quran describes the Prophet (peace and blessings be upon him) as a ‘mercy to creation.” This mercy is unlimited for it includes teaching and guiding man to the straight path as well as promoting both his material and spiritual wellbeing. As such, this mercy was not limited to those who lived at the Prophet’s time, but extends throughout time. Describing the Prophet’s mercy, the Quran says, "To them and to others yet to join them" (Quran 62: 3)

Commemorating the birth of the Prophet (peace and blessings be upon him) is a manifestation of love
Commemorating the birth of Prophet Mohammed (peace and blessings be upon him), the seal of prophets and messengers, is among the best deeds and one of the greatest acts which brings us closer to God. This is because it is a manifestation of our joy and love for the Prophet which is one of the principles of faith. It has been authentically reported from the Prophet (peace and blessings be upon him) that he said, "None of you will [truly] believe until I am dearer to him than his father, son, and all humankind” (Bukahri). Ibn Rajab said that love for the Prophet (peace and blessings be upon him) is one of the principles of faith and is parallel to our love for God, the Majestic. God warns those who give precedence to things which are naturally dear to them such as relatives, wealth, and homeland over their love for Him and His Messenger. He said: "Say [Prophet], ‘If your fathers, sons, brothers, wives, tribes, the wealth you have acquired, the trade which you fear will decline, and the dwellings you love are dearer to you than God and His Messenger and the struggles in His cause, then wait until God brings about His punishment " (Quran 9: 24).

‘Umar told the Prophet (peace and blessings be upon him), “O Messenger of God! You are dearer to me than everything except myself." The Prophet (peace and blessings be upon him) replied, “No! By He in whose hands is my soul, [you will not truly love me] until I am dearer to you than yourself." ‘Umar then said, “By God, now you are dearer to me than myself.” The Prophet (peace and blessings be upon him) replied, “Now ‘Umar [you truly love me]” (Bukhari).

Commemorating the birth of the Prophet is equivalent to honoring him
Commemorating the birth of the Prophet (peace and blessings be upon him) is equivalent to honoring him, which is itself undeniably sanctioned in Islamic law since it is the first of all principles and their supporting pillar. God acknowledges the rank of His prophet, so He informed all creation of his name and advent and of his status and importance. The whole universe is eternally joyous with the light of God and His blessing upon His creatures. Celebrating the birth of the Prophet (peace and blessings be upon him) is an essential part of honoring him.
Since the 4th and 5th centuries after the advent of Islam, our predecessors have been accustomed to spending the night celebrating the birth of the Prophet (peace and blessings be upon him) by engaging in many kinds of acts to bring them closer to God Almighty. They held banquets, recited the Quran, made dhikr (remembrance of God) and recited poetry and eulogies on the Prophet (peace and blessings be upon him). These activities were recorded by several historians, including scholars of hadith such as Ibn al-Jawzi, Ibn Kathir, Ibn Dihya al-Andalusi, Ibn Hajar, and Jalal al-Din al-Suyuti (may God have mercy on them). The majority of the scholars from among our predecessors and their successors clearly stated the legitimacy of celebrating the noble birth of the Prophet (peace and blessings be upon him).

Books on the subject
A group of scholars authored books commending the commemoration of the birth of the Prophet (peace and blessings be upon him) and used authentic evidence to demonstrate its recommendation, leaving no doubt to any sane person on the permissibility of the practice of our righteous predecessors. Mentioning valuable remarks on the topic, Ibn al-Hajj described the advantages of celebrating the birth of the Prophet (peace and blessings be upon him) in great length in his book Al-Madkhal the subject of which was the condemnation of innovations for which there is no evidence in Islamic law. Likewise, Imam al-Suyuti wrote a separate treatise which he entitled Husn al-Maqsid fi 'amal al-Mawlid.

Means of celebration
People customarily celebrate this occasion with buying and gifting sweets. Gift giving is a recommended act in itself and there is no evidence for its permissibility or its lack thereof concerning a particular time. Furthermore, if we add to this other righteous objectives such as bringing joy to the members of one's household and maintaining ties of kinship, it becomes even more recommended and meritorious, especially if it is an expression of one's joy at the birth of the Prophet (peace and blessings be upon him). This is because the means have the same rulings as the ends and opinions maintaining its prohibition or which seek to prevent its celebration are considered reprehensible and excessive stringency.
Some people doubt the permissibility of celebrating such occasions due to their absence in the early centuries of Islam. Even if this were true, it does not justify preventing the celebration of the birth of the Prophet (peace and blessings be upon him). No person could doubt the joy of those who lived at that time (may God be pleased with them) over the Prophet’s birth.
There are many means of expressing joy which is not an act of worship in itself, and there is no objection to choosing any one of these; therefore it is permissible to express joy at the Prophet’s birth in individual ways. Our predecessors celebrated the Prophet’s birth in various ways; they held banquets, recited the Quran, made invocations, and sang poetry and eulogies on the Prophet (peace and blessings be upon him) and his household.
There is evidence in the Sunnah that the Companions celebrated the Prophet (peace and blessings be upon him) with his acknowledgment and permission. Burayda al-Asmali (may God be pleased with him) said that once after the Prophet (peace and blessings be upon him) had returned from one of his conquests, he was approached by a black slave girl who told him, "O Messenger of God! I vowed to beat the duff and sing before you if God returned you safely." The Prophet (peace and blessings be upon him) replied, "If you made a vow, then go ahead, but if not, then do not beat the duff" (recorded by Ahmed and al-Tirmidhi who declared it an authentic and singular hadith). Thus, if beating the duff to express joy at the Prophet's safe return from battle is permissible and he acknowledged it and commanded the girl to fulfill her vow, then expressing joy over his birth by beating the duff or any other permissible means is even greater and more desirable.
A tradition in the Sahih of Bukhari states that God reduces Abu Lahab's torture in Hell-fire every Monday by allowing him to drink from the depression of his palm in spite of being a stubborn unbeliever and an enemy of God and His Messenger. This alleviation from torture is due to his joy over the birth of the best of humankind, expressed by his manumission of his slave girl Thuwayba when she brought him the glad tidings of the Prophet’s noble birth. Imagine then the reward of God to the believers who are overjoyed over the Prophet's birth and the radiance of His light upon the universe!

The Prophet taught us how to commemorate his birth
The Prophet (peace and blessings be upon him) recommended the nature of thanking God Almighty for his own noble birth. It was recorded in an authentic hadith narrated by Abu Qatadah that the Prophet (peace and blessings be upon him) fasted on Mondays and said: “I was born on this day” (Muslim). The fast is in gratitude for God’s favor on him and to the [Islamic] community by his very presence. It is even more appropriate for the community to follow the Prophet’s example in thanking God for His benefaction by all expressions of gratitude such as feeding others, chanting eulogies, assembling for dhikr, fasting and praying the Night Vigil prayer — each expressing his gratitude in their own way.
Subul al-Huda wa al-Rashad fi Khayr al-'Ibad, the Prophet’s biography, cites a righteous man from among his contemporaries saying that he saw the Prophet in a dream and complained to him that some pseudo scholars maintain that commemorating the birth of the Prophet is an innovation in religion. The Prophet (peace and blessings be upon him) told him, "I am pleased with whoever is happy with my birth."
We are blessed with the Prophet's coming into existence which is the cause for every blessing that has come upon man from that day on. Thus, commemorating that day and being reminded of it is a means for demonstrating our gratitude for the blessings of God upon humankind.
And God Almighty knows best.