Cookies are generally safe.
They are not programs they are small text files.
They keep details of your userid and password so you dont need to logon each time, plus maybe keep details of when you last visited, or maybe your name.
So if you revisit a website it may say "Welcome back Fred, you have not visited us for a few days".
If you DONT let them save cookies you may find the internet becomes a bit of a pain having to logon each time.
Personally I am getting sick to death of pressing "I accept" on loads of web sites. There should be a default setting on in your browser which just says "I accept" to save you have to press it.