How to repair damage to MDF baseboard trim
That looks like MDF baseboard, which is very porous and will swell when it gets wet.  It looks like there was a way for the water from your mopping to wick into the baseboard (likely a nick or cut in the factory finish).

To repair the paint, you'll need to sand the swollen part down flush to the surface. If you find yourself having a hard time getting it smooth or the fuzziness doesn't go away after sanding, skim the top of the damaged area with very thin layer of wood putty and feather it out, then sand smooth.

MDF likes to suck up paint too, so I'd use an oil based primer before finish coating.  It's possible that the paint might raise the surface a tiny bit and make it rough after priming, so lightly sand with 200 grit sandpaper after the primer is fully cured.

Finally, make sure that you don't have to repeat this process at some point in the future.  If this is in an area where there is a good chance the floor will get wet, make sure the caulking between the baseboard and tile is sound - particularly where the grout lines run underneath it.