The asterisk is largely used by editors to guide readers towards previous issues where events related to the current story take place, such as an origin story, the first appearance of a character, a team-up between heroes, a cross-title appearance or the last known whereabouts of a villain. It would also inform the readers of little known facts that were pertinent to the plot of the story.
During the mid to late nineties, Marvel titles had an overflow of editorial notes where a page would contain multiple asterisk boxes and the book itself would have up to a dozen, whereas ten years prior, there would be two to three if any at all. After Joe Quesada took the reigns as the editor-in-chief at Marvel, the use of editorial notes where taken down drastically.
The asterisk is also used to inform readers what acronyms like S.H.I.E.L.D., A.I.M., B.P.R.D., and such stand for.
In recent (and not so recent) years editors have used the asterisk box to add a little humor and do some infighting between editors over things a normal comic fan would.