HLA-B27 is a member of what are called the Class I MHC proteins, which are found on most cells in the body.

The main job of Class I MHC proteins is to help defending against virus infections. When a cell is infected with a virus fragments of proteins made by the virus will end off bound to Class I MHC proteins on its surface. These are recognised by immune system cells (cytotoxic T cells) which kill the cell, stopping the virus from replicating.

However, sometimes this goes wrong. Inheriting HLA-B27 is a risk factor for ankylosing spondylitis, which is an inflammatory auto-immune disease. Essentially what happens in this case is that cytotoxic T cells "make a mistake" and kill normal body cells, "thinking" that they are infected with a virus.

As far as I can see (a PubMed search) inheriting HLA-B27 is not a known risk factor for myasthenia gravis.

I hope this is not too technical and trust that it makes sense.