To transgress means to break a law or a rule. When we do something wrong, we transgress. When Adam and Eve lived in the Garden of Eden, Heavenly Father commanded them to not eat fruit from the tree of knowledge of good and evil. Adam and Eve were tempted by Satan and ate the fruit. Heavenly Father cast Adam and Eve out of the garden because they transgressed.
All of Heavenly Father’s children are given the agency to choose right or wrong. He has promised us blessings when we choose the right. Heavenly Father wants us to return to live with Him again. If we make bad choices, we need to repent and do better. But Heavenly Father does not make us repent for the bad choices that others make. We are responsible for our own actions.