Even for those not performing the pilgrimage, Hajj, the first ten days of this month are considered very sacred and a time for increased reflection, seeking Allah's forgiveness, doing good and various other forms of worship.
Muslims who perform the Hajj or Umra must run in the middle portion of the distance between Safa and Marwa seven times. This is a commemoration of one mother's sacrifice for her son.
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.