This is one of the most amazing museums in the world today--and there are a LOT of spectacular museums. It pretty much has the history of the world, from pre-civilization to modern times, all under one roof. What is equally amazing is that the museum continues to be free of charge, not counting the special exhibits.
A large chunk of the museum is dedicated to the collections from ancient Greece and Egypt. The collections from these two areas are absolutely fascinating, and the descriptions given on the artifacts are diligently done. One of the highlights in this part of the museum is the famous Rosetta stone, which allowed archaeologists to understand and translate hieroglyphics.
I found that the best way to explore the museum was to come back a few times and only spend a couple of hours at a time. That way, you will not be overwhelmed with the large number of galleries you will need to see or numb with information and sensory overload. A visit to London should include the British Museum without fail. It is both grand and fun.