Unicellular or single-celled: made up of just one cell (bacteria, protozoa, many algae, yeasts).
Multicellular o pluricellular: made up of more than one cell: (some algae, most fungi, plants and animals).
All cells are able to perform the three vital functions:
(a) they reproduce, quite usually by mitosis, a process that yields two daughter cells with almost identical genetic material;
(b) they interact with their environment, giving responses to specific stimuli, as when a white blood cell is able to detect and destroy a bacterium;
(c) they feed, meaning that they are able to exchange matter and energy with their environment, as when a human cell takes oxygen from the blood and releases carbon dioxide.
All the cells have:
A cell membrane, the cellular envelope: the thin layer which separates the inside of the cell from its surrounding environment. It encloses the cell and regulates the substances exchanged between the inside and the outside of the cell.
A cytoplasm with organelles, which are specialized cell compartments where specific functions are fulfilled.
Genetic material, that carries the instructions that allow both the cellular work and its self-construction. This hereditary information of living beings passes from one generation to the next.
Kinds of cells
There are two main kinds of cells, according to the genetic material:
The cells of the bacteria and archaea have no real nucleus: they are said to be prokaryotic.
(Diagram of a typical prokaryotic cell from wikipedia)
The cells of all the other living beings (algae, protozoa, fungi, plants and animals) have their genetic material separated from the cytoplasm by a nuclear membrane: they are said to be eukaryotic.