A table change is a request from a player to move from one poker table in a casino to another, in the same casino. In most cases, this also means moving to another table of the same variant and stakes, though players will occasionally use "table change" to mean changing to a table of a different variant or stakes.
In a casino, the floorman is in charge of table changes, and must generally approve them and have them scheduled with the brush before they can take place. This is because one of the floor's duties is to ensure that no games get particularly shorthanded, so if a player's table change would cause a table to become shorthanded, the floorman may deny their request.
Players making a voluntary table change are generally not treated any differently at their new table than a new player arriving to play for the first time. For casinos which require new players to post, these new players must also post, minimum buy-ins must be respected, and so on. This differs from a table change which is happening involuntarily on the part of the player (e.g. from a broken game).
Players will request table changes for a variety of reasons. Superstitious players may change tables if they believe the table, or the current dealer at the table, is "unlucky" for them. Observant players may change tables if they feel the competition at a different table is weaker, and thus more profitable. And, of course, any player may request a table change if social or other conditions at the table are making it unpleasant for the player to continue playing there (e.g. a drunken boor yelling a lot, a nearby player with a foul odor, an escalating personal argument between two other players, etc).
Note that table changes are different than seat changes, a much simpler procedure that does not require the floorman's approval.