All cells do not necessarily have a nucleus. Cells with a defined nucleus are called eukaryotic cells, while cells possessing no nucleus are called prokaryotic cells.
Eukaryotic cells have a defined nucleus, otherwise called the "brain" of the cell. This nucleus is surrounded by a membrane which separates the nucleus from the other clearly defined parts of the cell, called organelles. Examples of organelles are mitochondria and chloroplasts. Eukaryotic cells have the ability to become any type of tissue, based on their specific DNA.
Prokaryotic cells do not have a defined nucleus with a membrane, and typically lack the organelles of a eukaryotic cell. The DNA is contained within the cell walls in a random fashion. Due to the lack of organization, prokaryotic cells are extremely limited in size and are typically hundreds of times smaller than the average eukaryotic cell. The most common example of prokaryotic cells is bacteria.