Protozoa are single-celled creatures with nuclei, usually showing some animal-like characteristics such as heterotrophy and motility and so originally classified in that kingdom. There was never really a sharp dividing line between them and the plant-like algae, though, so many forms were included in both. Now it is understood that Protozoa and algae are neither plants nor animals, and they are given their own kingdom, the Protista.
The traditional division of protozoans is on the basis of movement, and while this is no longer believed to represent true relationships, it's still a useful way of organizing the many different groups:
Most protozoans are too small to be seen with the naked eye - most are around 0.01-0.05 mm, although forms up to 0.5 mm are still fairly common - but can easily be found under a microscope. Protozoa are ubiquitous throught aqueous environments and the soil, and play an important role in their ecology. A few are also important parasites.