Winning the popular vote means that a lot of people voted for that candidate. To me it indicates that it was a very close election.
Edit: Data from here: https://ballotpedia.org/Voter_turnout_in_United_States_elect... (notably PA and WI are missing)
Maybe you could say states that transition from being safe to swing states see a turnout boost? I haven't checked. I would expect that turnout is more determined by demographics and inertia (states with high turnout in prior elections continue to do so, etc) than whether they are swing states, though.