Tags are words or phrases used to describe something in a computer system.  In Brainstorm, we use tags to better understand the ideas and people that use Brainstorm.  For example, if you submit an idea that your organization should replace disposable paper cups with mugs to reduce cost and help the environment (what some folks call going "green"), you might add tags like "cost reduction," "kitchen" or "green." 

We use that understanding to connect ideas with the people that can help move the ideas forward.  In the example above, we could connect that idea to someone who is interested in "green."  We also connect ideas with other similar ideas that may have something worth sharing with each other.  And we even connect people with other similar people.  I think you get the point.  It's about connections.  Tagging your ideas or your own skills and interests will help Brainstorm to connect you with the information that's most relevant.

And, if you really want to get into it, check out the Wikipedia explanation of tags.