Can anyone tell me about this application?
It's rather popular these days. I read some things, but I would like some more info about its usage and usefulness. :)
Generally, it's a document management tool. While it can support extras, like workflows, at the end of the day the heart of it is providing a location to store documents and work on them collaboratively. It supports change controls so if someone comes in and "poorly edits" a document it can be reverted back to a previous copy. It supports permissions, as well as sharing with 'external contacts' (those outside the organization).
Depending on how large the organization is and/or how willing folks are to use it as it's intended, this can either be an awesome tool or a giant pain.
Wikipedia does a good job of giving the layout of the land: https://en.wikipedia.org/wiki/SharePoint
Anything specific you were looking to understand better?