What does the BASESP dash light mean on a Mercedes ML320?

It means it has an error, it can be several things. Hopefully it is just a sensor error which is cheap to fix vs a new computer system which can run $2k plus. Best bet is to replace the brake position sensor first and if that does not fix the problem then you have to go to the dealer and have them diagnose the car for you, most dealers will do that for free and if it seems like an easy problem that you can fix just buy the parts and make it an afternoon DIY.

After replacing the break switch if problem continues to exist then replace the relay that can be found under the hood inside the fuse box. look for (esp/bas or I guess #38).