Aparigraha is the concept in which possessions should include only what is necessary at a particular stage in one's life. It is a form of self-restraint that avoids the type of coveting and greed by which material gain destroys or hurts people, other living things or nature in general. Aparigraha is the opposite of parigraha, which means "the focus on material gain."
Aparigraha is one of the main lessons in the Bhagavad Gita, which states that a yogi should give up possessions that hinder his/her yogic path. Doing so frees the yogi from dependence on sensual and bodily demands, allowing experience of the true Self at a deeper level.
In the context of a yoga class, aparigraha is the acceptance of what the body is capable of doing while practicing, rather than the desire to perfect a pose as someone else has.