What will be the proper answer for this question:
"How does SharePoint work?"
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That is about the same as asking "how long is a piece of string?". SharePoint is not a product that "does" anything in particular. There are a few things that come with SharePoint out of the box, without any consideration of what your company actually needs, but in most instances that will not be how YOU and your company may want to use SharePoint.
SharePoint is an egg-laying wool-milk pig.
It can be anything you want it to be, depending on how much effort, budget and resources you are prepared to throw at it.
So, SharePoint works however you configure it to work. You can make it to be
The basic mechanics of SharePoint include SQL Server as the storage system and IIS for presenting the web site. But there are so many layers and services that influence just exactly WHAT SharePoint does and HOW it works, that this is too much for a single question.
You should NEVER just install SharePoint and then wonder what to do with it.
The better approach would be to analyze your business needs and then evaluate IF SharePoint can be applied to solve one or more of these business needs. There may be other systems more suitable for your business situation. Or SharePoint may be a good starting point.
Excuse the rant.
First take a look at: http://www.aiim.org/What-is-Microsoft-Sharepoint This will help get you on the right path.
Then if you want to know more you can take a look at Wikipedia: http://en.wikipedia.org/wiki/Microsoft_SharePoint
And if you're still curious and need to ask more general questions from there then communities like http://reddit.com/r/sharepoint are good ones to ask more general discussion orientated questions (this community is more for direct trouble shooting or specific issues).