To answer the main question, https://confluence.atlassian.com/agile066/glossary/story-point
The picture you've posted is a little hard to explain without a little bit of background. I'm going to oversimplify this a bit too, and leave stuff out. The idea behind Scrum is that you've got a pile of stuff that needs doing broken up into issues. You put estimates on these issues, then you break up your time into "sprints". For each sprint, you grab some of your issues and commit to delivering the work that is needed to do them within that sprint. Then you measure how you get on, and that helps inform you how you should be estimating/working on the next sprint.
To do that, you need something to estimate on. JIRA Software lets you estimate on time, or story points, or in fact, any other numeric field you might want to use. Anything that can be quantified really.
Going back to your screenshot now. Those three coloured blobs are a simple sum. They add up and display the estimate for the current sprint. There are three colours there because it breaks the issues up into the categories that their status is in - blue is "to do" (you have not really started any work on them), yellow is "in progress" and green is "done".
You are getting empty coloured blobs because you either have no estimates, or your board is looking at the wrong estimation field. If you have filled in story points, or time, or another number, then go to the board configuration -> estimation, and select an "estimation setting" of the field you want to use.
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