The eminent Muslim scholar and renowned Da`iyah, Sheikh `Abdel Khaliq Hasan Ash-Shareef, states: It is a part of the Prophetic Sunnah for men and women to clip the nails. The Prophet (peace and blessings be upon him) is reported to have said: “The fitrah is five things: circumcision, removing the pubic hair, trimming the moustache, cutting the nails, and plucking the armpit hairs.” In addition, we are recomended not to leave our nails without cutting more than 40 days. Anas (may Allah be pleased with him) said: “The Messenger of Allah (peace and blessings be upon him) set a time limit for us to cut our moustaches, cut our nails, pluck our armpit hairs and shave our pubic hairs: we were not to leave it any longer than forty days.” (Reported by Ahmad).
Thus, you are recommended as a practicing muslim to cut your nails according to the Sunnah of the Prophet after this period of time. The reason behind this is cleanliness and hygiene, because dirt can gather under the nails.