to sin, to do wrong: to fall short of what God or a relationship requires, incurring guilt
The root idea is missing a mark or going off the path. A single occurrence in Judges captures the literal edge: seven hundred left-handed Benjaminite slingers who could aim at a hair and "not miss." The moral use takes that physical image and applies it to the whole range of human failure, falling short of God's commands, offending another person, betraying a trust. It is the Hebrew Bible's broadest, most direct word for moral and relational failure.
The word covers both the act and its aftermath. Someone who sins bears something: a guilt, a record, a weight that must be addressed. This is why confessions so often run "I have sinned" and immediately move to a plea for pardon, the act and the accumulated burden travel together. It is used in the starkest first-person admissions (Pharaoh to Moses, David after his census, Peter's ancestors in Nehemiah) and in communal prayers that acknowledge the nation's accumulated wrong before God.
A common use in Kings and Chronicles is what scholars call the "Jeroboam formula": a king "caused Israel to sin" by perpetuating the calf shrines at Bethel and Dan. This causative form means leading or enticing others into sin, and the Books of Kings repeat it as a drumbeat across the divided monarchy to explain the nation's downfall.