Trossie,
A seniority system is a list of pilots, usually based on the date they joined the company. An argument for it is that it is difficult to pick a pilot for promotion to a bigger aircraft, command etc. any other way, since all pilots theoretically posses the same skills. It can also govern such things as bids for routes, days off etc. My old company used to have a separate list for Captains and First Officers. A F.O. on promotion would join the bottom of the Captain's list. It had the advantage that crewing for the less popular types (generally turboprops) was easier, since it was worth a few years on that type in order to be on the list. Once it was abandoned, many F.O.s stayed in the RHS until senior enough to move directly to the LHS of a jet. Conversely, in the event of redundancies, it was also of course an ideal "last in, first out" list.
Generally, airlines like the system (or at least did when I was active) since it helps retain pilots. The move to the bottom of another company's list isn't so attractive.
I'm sure things have changed in the years since i left the business, with the growth of the LoCos, P2F etc, but the basic principle is here. Current pilots, please update this.