It doesn’t really do much, as the version number suggests.
Nintendo has silently launched a brand new update for the Nintendo Switch, a bit over a month after the previous update came out. Unlike Update 6.0.0, however, which was a relatively major one as Switch updates go, Update 6.1.0 is far more incremental and minor—which the version number should have tipped you off about.
It doesn’t do much—it just addresses a glitch where certain games didn’t recognize right away that you have a Nintendo Switch Online subscription (which, if you will remember, is needed to play online on Nintendo Switch now). It also adds some “stability” to the console, which presumably means some under the hood changes, and some patching up of security exploits.
If your Switch has auto updates on, and is in Sleep Mode, the update should have downloaded automatically, and all you have to do is apply it when you turn it on next. Otherwise, you can always force a download and install by going to System Settings, and searching for an update from there.