what is the difference between the Twitter streaming API and REST?

I am still new to social media development. At work, we had some wrapper class that retrieves tweets manually, but that was done using the Twitter REST API.

Since then, I did some research on my own. And people have suggested if I worry about rate limit, I should try the streaming API.

I checked out the streaming API on Twitter, but it doesn't really tell me much other than a high level overview, which I understood.

So I am just wondering, what exactly is the advantage of using Twitter Streaming API over REST? And what is the difference between the 2?

Please advise. Many thanks