What does it mean to have high immunoglobulin G levels?

High IgG levels does not lead to a diagnosis without further details of the types of IgG which are elevated. An increase in certain IgG subclasses is associated with diseased states especialy IgG4 in allergic diseases, asthma and cystic fibrosis. With the wording used in the question it could imply that the person is mearly at the outlying area of normal distribution (reference range), just as some people are "tall" some people have naturally high IgG titers. On the plus side a high IgG titer means it is highly unlikely (but not impossible) that the patient has any immunodeficient diseases associated with IgG.