Laxity is a tendency of being too easy-going, or not strict enough. If your teacher doesn't punish her math class for climbing out the classroom windows, she may be accused of laxity.
A government's laxity with regulations can result in big companies taking advantage of the situation. Likewise, a babysitter's laxity with his young charges can result in mayhem, or at the very least an extremely late bedtime. A physical kind of laxity is a literal looseness, especially of muscles and ligaments: "If you over-stretch before your run, your muscles' laxity can harm your joints." The Latin root is laxus, "loose."