The seniority system in Congress grants privileges, such as choice of committee assignments or choice of office, to the members of congress who have served the longest. It is normally seen when deciding who is going to be a committee chairman. The longest-serving member of the committee gets the choice of becoming chairman first.
Congress is made up of the Senate and the House of Representatives. Because Senators have 6-year terms and Representatives only have 2-year terms, the seniority system is most prevalent in the Senate. The seniority system has been criticized because it does not necessarily mean that the most qualified person will become chair or get privileges. Instead, it just means the most senior member of a committee gets privilege of choice over other members.