There are 3 types of these that are prevalent.
1) Remakes -- these are built from the ground up for newer technology with completely new assets, but are otherwise identical to the original designs. Tomb Raider Anniversary is a great example. I believe FF7 is going to be like this as well. Ratchet and Clank PS4 is another example.
2) Reboots -- Same name, different game. In the spirit of the original, but its own game. Great example again with last gen Tomb Raider.
3) Remasters -- Take an original game and upscale it to a higher resolution. Game is otherwise unchanged. This practice is what a lot of gamers get upset about. Halo. Uncharted. God of War. The Last of Us. The list goes on. The entire game is scaled and optimized, but it's the exact same game.
I just want to experience something new and fun!