Intranet:
A network within a company, not reachable from the outside world, it's mostly used to share information. It uses Internet-techniques and could be described as a "small Internet".
Extranet:
Is an Intranet that has been opened up for customers, partners etc. so that they can access information even if they're not connected directly to the private Intranet.
LAN stands for Local Area Network. It is typically a group of computers connected to a network within a building.
Check out www.whatis.com, it's a great resource when you are wondering what a computer related term means.