The kingdom Protista started out in the three kingdom system to "solve" the problems of the two-kingdom system of animalia (animals) and plantae (plants). Bacteria, eukaryotic single celled organisms, and fungi are not quite plants or animals, so the two-kingdom system was not really effective. With the three-kingdom system, anything that wasn't quite a plant or an animal was put in kingdom protista. This wasn't much help either, as bacteria, fungi, and single-celled eukaryotes are still quite different from eachother. So a five-kingdom system was created, consisting of animalia, plantae, fungi, monera (bacteria), and protista. This solved many of the problems with the two and three kingdom systems, and is the system in wide use today. Protista still remains a quite inclusive kingdom, as it includes a diverse selection of organisms.
In the five-kingdom system, protists have the following characteristics:
Eukaryotic cell(s)
Usually unicellular (seaweeds and related organisms are multicellular)
Usually reproduce asexually (although sexual reproduction is possible for some species)
Can be either autotrophic or heterotrophic
They live in aquatic environments