A covenant is a sacred and serious promise given in association with specific ordinances that are essential to a Mormon inheriting eternal life. LDS covenants are always bilateral and conditional on the obedience of the person. For instance, Mormons will make a covenant when they are baptized and renew their covenant when they partake of communion. Covenants are agreements that if Mormons promise to do their part (obedience), then God will do His part (blessings).
“A covenant is a sacred agreement between God and a person or group of people. God sets specific conditions, and He promises to bless us as we obey those conditions. When we choose not to keep covenants, we cannot receive the blessings, and in some instances we suffer a penalty as a consequence of our disobedience.” (True to the Faith, p. 44)
When Mormons choose to receive their endowments at the temple, they are entering into a very serious covenant with Heavenly Father. If they choose not to be obedient in their promises, or worse, end up rejecting the teachings of the Mormon Church, then the consequences are severe.