What do elevated levels of IgM mean?

Depends. The "normal ranges" for all lab tests include 95% of the "normal" population; thus, 2.5% of people are above the upper limit, and 2.5% are below the lower limit. There's nothing to worry about if your values are a little bit above the normal range, but a very elevated IgM could be a sign of a problem. You need to check with the physician who ordered the tests to interpret your results.