Resolution refers to the number of pixels. In other words, its size. So, to make them higher res, you just make them bigger. High res is, I believe, 1600 pixels wide or 1200 pixels tall (this software may go by a different measurement). Anything below that is designated "<highres" and gets a black star.
It doesn't mean anything. It's mostly a warning. Because, if you click the star, it takes you straight to the full res image. The red star means "heads up, this pic is kinda big".