As an example, in WordPress blogs, you might see a list of 25 comments in your Dashboard. Next to each one will be a checkbox. You can go down the list and check, let's say, 15 of those comments as spam. And then you can click "Bulk Action" before the next action you apply – Trash, Report as Spam, etc. – so that your action will affect all the comments that you have selected ... not just one comment.
So you can perform one action – Trash Comment, for example – on a "bulk" of messages. It's a way of speeding things up.
Other members may have better, or more succinct, examples.