A poker game is generally considered shorthanded if there are 5 or fewer players playing at the table, though some casinos consider slightly different cutoff levels (e.g. 4 or 6 players).
In general, casinos don't offer shorthanded games. If a game drops to 5 or fewer players through natural attrition (players getting up to leave), it will generally stop and the casino management will attempt to either find new players for the empty seats or find other seats at other active games for the remaining players to join. When this happens, and a table is stopped and its players are sent off to join other tables, it is called a broken game, or sometimes a broken table.
Shorthanded play is slightly different from a normal ring game, strategically: the blinds come around much more frequently which forces players to play a much wider range of starting hands than they would normally do in a larger group.
Shorthanded play is rare enough that it can be a tricky skill to get practice in. In physical casinos, shorthanded play generally only occurs towards the end of tournaments, when either there are just barely too many players for one table (e.g. 11 players left at 10-player tables, so one table has 5 and one table has 6 until another player busts out), or there are only a few players remaining in the tournament.
However, some online casinos have recently instituted special tables which have a limited number of seats (usually 5 or 6), to force shorthanded play to occur. Since the table is limited to at most 6 players, all play at the table by definition is shorthanded. This has attracted a number of players who want practice in this skill, as well as those who are already skilled in this area. It also attracts some looser "gamblers" who feel that the extra play shorthanded tables force on players makes for looser and more lively action, which may be more attractive to them personally.