The main purpose of fasting is described in the Quran as "so that you may attain Taqwa or God-consciousness." Fasting is thus yet another instrument for bringing us closer to our natural state, our state of Fitrah.
These are a series of excerpts from Abdul Wahid Hamid's book "Islam: The Natural Way", an excellent guide to the Islamic worldview and lifestyle, particularly for Muslims born and/or raised in Western countries.
Sacrificing certain types of animals during Hajj and Eid-ul-Adha are part of Islamic rites. Here is Muslim American Michel Jansen's experience of apprehension towards Islamic animal sacrifice during Hajj and how she reconciled herself to the rite.