Typically the game saves are in a different folder to the game. So while you may delete the game, the game saves still exist on your hard drive. When you play the game again - it finds those game saves and reuses them.
For example, when my game starts, it will look for a save file. If the save file exists, it uses it. If there is no save file, it creates one. These files are usually stored in a location like Appdata that is often hidden. That's not too be sinister, it's just the way Windows works.