If you're talking about research requirements in the residency program description, they're referring to research you do during your residency. ACVS requires a first-author publication of original research related to surgery, and many other specialties have similar requirements. Some residencies have additional publication or research requirements during your residency. You don't really need to worry about that now. In fact, for ACVS the publication can't be more than 5 years old at the time of credential submission.
To be honest, they're all kinda the same. Everyone is president of this or that club, went on a RAVS trip, mountain bikes and fed the homeless ... yawn.
If you could pick up a Nobel prize along the way that would be good, but otherwise I would do things you really enjoy, not because you think it will look good on an internship/residency application.