See Closure on Closures (and also How A Function Becomes Higher Order and How To: Make An Iterator) and their various 'Reply' and 'Also' sections for applications, amplifications, etc.
I don't think I could come up with an explanation better than the above or than those contained in standard references. If you still have problems, you might try asking specific questions – with examples, if possible!
BTW: I put these refs. together using Super Search on 'closure'!
Update: Closure may also be helpful.