From Academic Kids
Law 6 of the Laws of the Game outlines their general duties, which are subject to the decision of the referee. These duties typically include indicating: when the whole ball has passed outside the field of play; which side is entitled to return to the ball into the field of play; when a player may be penalised for an offside offence; when offences have been committed which the referee does not have as good a view of; etc. The assistant referee may be called upon by the referee to provide an opinion regarding matters which the referee requires clarification on. The assistant referees also usually assist the referee with preparatory and administrative functions.
An assistant referee indicates matters to the referee, which the referee may then act upon; they do not actually make binding decisions.
Assistant referees were formerly called linesmen. The name change was primarily to better reflect the modern role of these officials, and secondarily to become non-gender specific. They are also sometimes incorrectly referred to as "referee's assistants".