This has to do with whether a question has an accepted answer, and/or whether your answer was accepted.
When you look at a list of questions, the icon is filled green if that question has an accepted answer. Consider these three from the list generated by the regression tag:
The first thread, linear regression with partially known coefficients, has one answer, which has been accepted. The last thread, How to calculate bias when we have an estimation using simple linear regression?, has one answer, which has not (yet?) been accepted.
When you look at your reputation page, you will see a filled green icon representing the reputation you gained from having one of your answers accepted. Here is a section of your reputation page:
When the reputation gains from August 14th are expanded, you can see that the icon is filled green because you received 15 points from when your answer to Is there such a thing as an adjusted $R^2$ for a quantile regression model? was accepted (congratulations). Note that the reputation you gained from the upvote is not filled green.
Regarding the screenshot of your homepage, On round robin is green under questions because it is a question with an accepted answer. The square isn't green under reputation because you didn't earn that 5 points of reputation by having an answer accepted (but by having your question upoted).