This is actually two museums, one relating to medieval medicine and hospitals and the other to artwork. They make a pretty good combination.
The entire museum is housed in a former hospital dating back to the 1300s. The hospital display part makes you happy for modern medicine. One of the most persuasive things in that regard is painting of an eye surgeon working on a hapless young patient, with primitive tools and no apparent compassion.
The art part is taken up mostly with the art of Hans Memling, a great German artist. There are also several other medieval pieces. Most visitors won’t be familiar with the works (we were not), but they are worth seeing. The Ursula Shrine is considered a masterpiece. Note in particular the very fine details on many of the paintings – one even goes off the canvas onto the frame.
Note that there is a pharmacy in a nearby structure that is part of the museum. It's worth a 5-10 minute look. If you do, look closely at the carvings on one cabinet - it's of an apothecary that is very much like the one you are standing in.
Before you visit this attraction, consider getting a Bruges museum card (you can get them at the tourist information offices or some of the museums). If you are stopping at several Bruges museums, it can save you some expense. They are good for three days and also good if you stumble across a museum you hadn't considered that looks interesting.