The primary characteristic of eukaryotic cells that is absent in prokaryotic cells is the presence of a nucleus. Eukaryotic cells contain membrane-bound organelles, including the nucleus, where genetic material is housed. This allows for greater complexity and compartmentalization of cellular functions. Prokaryotic cells, on the other hand, are simpler and lack membrane-bound organelles. This distinction contributes to the diverse functions and forms of life present in eukaryotes, ranging from unicellular organisms like yeast to complex multicellular organisms like plants and animals.