what is sharepoint
Sharepoint is really two different technologies: Windows Sharepoint Services (WSS) and Microsoft Office Sharepoint Server (MOSS). WSS is free and it comes with Windows Server 2003. MOSS isn't free.
WSS provides lots of out of the box functionality for managing documents and projects online. It manages documents in "document libraries." These are folders with permissions and different views of your documents. Projects, tasks, issues, or any tabular data, is managed in lists. Lists are similar to document libraries. They have permissions and views as well. It provides some simple search as well.
MOSS provides a better search (it's supposed to at least). It also has more publishing capabilities (WSS doesn't). And you have more control over page layouts. It's meant more for internet style sites while WSS is more for intranet sites.
and why is it popular?
WSS is popular partly because its free and partly because it just does so much out of the box. You can solve many common office requests with WSS. Stuff like issue trackers, project management and document management are trivial in WSS. That said, its a jack of all trades - good at many, master of none.
MOSS is probably less popular because its not free and having used it for a year, I don't see as much value in it as WSS. Search isn't that great. It does do a good job of creating a company directory.