The SAV file isn't actually a save state - that could be compared more to a saved game. It contains info on your settings, and which levels you've beaten, so that it'll remember next time you load. It also saves the highest number of lemmings you've saved, fastest completion time, and highest score achieved for each level - you can view these by pressing R (I think) on a level's preview screen.
The save state feature only works while playing a level. Press Enter, then later press backspace during the level, and it goes back to that point. Once you exit the level, the save state is cleared. If you want something that carries over, you might want to use replays - press U during gameplay (or on the post-level screen) to save a replay file, then you can press L while playing that level to load the replay. This won't take you back instantly to a specific point, but will repeat every action; you can interrupt it at any point by performing an action (or if you just want to interrupt without specifically doing anything, click in midair).
