An interest list is a list, kept by the brush at a poker room, of players who are interested in playing a particular variant of poker for some particular stakes when such a game is currently not being spread in the card room.
Some casinos regularly open interest lists for all sorts of games, and allow players to sign up on multiple lists. Once enough players have signed up for a particular type of game, the casino will usually set one up and announce the players who can play (generally the first names on the list, up to the number of seats available at the newly-opened table).
The major board software companies all provide interest list features in their software.