In a Nutshell: Islam teaches that human life has a clear, divinely ordained purpose: to know, worship and serve Allah (God) while acting as His khalifah (steward or vicegerent) on earth. The Quran states explicitly that God created human beings and jinn for the purpose of servitude (Quran 51:56), but this servitude (ibadah) is understood broadly - it encompasses all ethical action, the pursuit of knowledge, the building of just societies, the care of the natural world and the cultivation of one's character.
Islam thus presents a vision of purposeful existence in which the spiritual and the practical are inseparable: every act of kindness, every honest transaction, every effort to establish justice is an act of worship when performed with the right intention. This life is understood as a test (Quran 67:2) and a preparation for the akhirah (afterlife), where human beings will be held accountable for how they fulfilled their responsibilities.
The Islamic answer to the question "why am I here?" is therefore simultaneously theological, ethical and practical.