Most games push you to survive, but not many make you simultaneously and legitimately fear for your life.
Survival Horror games, on the other hand, do.
Perhaps best described as interactive horror, Survival Horror has grown from a mere catch phrase in Resident Evil games to a genre all its own. The point is to scare the socks off you using any means necessary, whether those means include shambling zombies, grotesque figments of the imagination or twisted humans.
Survival Horror's beginnings are generally credited to the first Resident Evil game, though it did have a few predecessors in Sweet Home and Alone in the Dark. They established a formula for later games developed not just by Capcom (who capitalized on the genre in the first place) but other companies, as well: the player, plopped in a gloomy and horrific situation, is left to protect their character's life with a minimum of help.
Consequently there are few restorative items in Survival Horror games, and weapons to fend off the various horrors are scarce. The idea is to leave the player feeling exposed and vulnerable. More, though, the characters in these games are often much more frail than most adventure game protagonists, dying easily and requiring greater finesse with the controller. Throw in limited inventories and you're left with the obvious limitations of an everyday human fighting supernatural threats.
And those threats come from every direction. Like any good horror movie Survival Horror games thrive on the unknown. What lurks around that upcoming bend? What's that noise off in the distance? Will that manhole cover burst open if I go too close to it? A good round of Survival Horror isn't complete without plenty of paranoia, especially considering many of your fears will go unfounded and many other, seemingly harmless situations quickly turn deadly.
Survival Horror is, for some games, more than just a genre. It's a state of mind. The atmosphere, the music (or lack thereof), the constant threat - everything culminates in an experience that's just plain creepy. You're meant to enjoy the game, sure, but you're also supposed to fear the game. You need to keep on your toes or risk death, and you fear death because in a way that no other genre accomplishes, you thoroughly bond with your on-screen avatar. You'll fret for their safety as if your own health was at stake.
This feeling is further heightened if you play in the dark. I highly suggest you do, as a good Survival Horror game can provide more spine-chilling fun when played under the proper conditions than any horror movie.