I don't recall hearing the term except as part of infectious mononucleosis - a viral (Epstein-Barr Virus normally) disease most common in adolescents and young adults, characterised by swollen glands (hence it is aka Glandular Fever) and generally feeling pretty crappy. The mononucleosis part arises from the presence of a high number of mononuclear cells (aka lymphocytes) in the blood.

Literally then, I assume nucleosis is a high number of nuclei (with or without surrounding cells) in the blood, but there are much better terms for that.