There are several very important activities that are a part of closure. These include:
financial closure: all bills paid and revenues received
keeping of historical records: this is important to future project success
lessons learned: also important to future project success
By keeping good records of past estimates, plans, and other project history, you will be gathering information useful for other projects. I've often had team members say "I don't know how to estimate that" and then referenced data from a past project.