Soft lock is a video game term which describes a point in a game where a failure in either programming or design prevents the player from making additional progress in a game, but allows them to keep playing. The term comes from the older term "lock up" which describes when a computer program freezes or stops accepting input (itself based on an older meaning which described when a machine seized). Because you can no longer progress, the game is "locked," but, since the game is still running it's only "soft locked." An unavoidable soft lock is often described as a kill screen, regardless of whether it kills your character.
Many gaming sites refer to a game being "soft locked" if the player can't proceed without dying, but I think a soft lock should only apply when there are no in-game ways to get out of the lock. For example, some game sites describe "minus world" in Super Mario Bros. as a soft lock, since you're stuck in a repeating level. However, purposely dying or letting the time run out will eventually give you a game over which will return you back to the normal game state, ending the supposed "lock."
A subset of the soft lock is the unwinnable state which may occur in adventure and role-playing games. The difference being that a soft lock is typically obvious shortly after it happens and you're stuck in a very limited area, while it may take hours before you realize you're in an unwinnable state because you have access to much more of the game.
The video game hacker community has fixed many of the soft locks which can occur in the more popular video games.
In level 10 of the game Battletoads, you must race a rat down a shaft before it detonates a bomb at the bottom. Kicking the bomb before the rat reaches is will kill the rat, and it will fall down and shatter the floor allowing you to progress the game. However, a programming oversight makes it possible for the rat to sometimes fall through a wall preventing the rat from shattering the floor after you kick the bomb, keeping you stuck at the bottom. You can still move around, but, with no way to die or run out the clock, the game is soft locked and you're forced to reset. Being so far into such a difficult game, this is especially frustrating when it happens.
There are hundreds more examples listed on TVTropes, however, many of these are not true soft locks as the player can always purposely die or use an in-game reset.