The courtesy is as simple as leaving the basin dry and tidy for the next passenger. The last thing you want to see is a piece of booger in the sink, a giant spit with some blood or some other bodily fluids there. Other reasons might be:
- Dry sinks make the lavatories look cleaner, while wet sinks make the lavatories even when are clean they look dirtier.
- Leaving the basin dry and tidy is indeed a courtesy to passengers who put their stuff next to the basin (mobile, watch, etc.).
- Flight Attendants can not just leave everything and get busy wiping water and other fluids off basins, so this is better for passengers and airlines, because people will simply blame the airlines if lavatories found wet/dirty.
- The more wet the place is, the more better it is for bacteria to grow, and vice versa.
note: I assume basin here means the basin and the attached table.