I recently reinstalled Batman Arkham City on my pc through Steam and all of my saves are gone. What happened?

Doing a full reinstall of a game client will result in loss of saved games. It’s a recommended practice to back up your save files before reinstalling the game client.

To back up your save files:

Copy the content from: '\Steam\userdata\<id>\57400\remote folder' to another location on your computer. Now when you reinstall the game, your save files will be saved.