"Verify Integrity of Game Cache" - Right click on Skyrim -> Properties -> Local Files
If that doesnt work, it might be that the steam updated was faultly (it has happened to me before) and you can either wait for the next update....or reinstall steam.
Reinstalling steam:
1. Make a backup of all your games. File -> Backup and Restore Games. When you uninstall steam it remvoes all the games, so if you want ot save your bandwidth, you can back thme up to a folder on your computer.....the steam backup puts all the game into a single steam installer ready to install again later. TIP: When it asked for file size, select custom and tell it any huge size so that it all goes into a single installer.
2. Uninstall Steam. If the steam folder still exsists after uninstalling, delete that too.
3. Download and install Steam again.
4. Run your backup installler to put all your games back in.
There are properly instructionsl ike this onthe steam forums somewhere aswell which may have more details.