Kingdom Animalia is a category of mostly eukaryotic organisms. There are ten sub divisons or Phyla. Its recommended to by heart the names:

1.Phylum Porifera-Marine, and non-locomotive(eg:Spngilla)
2.Phylum Coelenterata or Cnidara-Mostly marine, sac-like(Hydra)
3.Phylum Ctenophora-Marine, one of those crazy aquatic things!(Ctenoplana)
4.Phylum Platyhelminthes-Some are marine, Flatworms(Tapeworm)
5.Phylum Nematoda-All types of habitat, complete worms(Ascaris)
6.Phylum Annelida-Marine,land,parasitic, worms(Leech)
7.Phylum Arthropoda-Mostly land, insects(Spiders,scorpion)
8.Phylum Mollusca-Marine, softbodied(Snail, Octopus)
9.Phylum Echinodermata-Marine, locomotive,spiny skinned(Starfish)
10.Phylum Chordata-All types of habitat,developed(You,me,fish,reptiles,etc)
All Phylums except the last, Phylum Chordata, are Invertebrates.
Chordata are verebrates and are devided into these:
Class Pisces
Class Amphibia
Class Reptilia
Class Aves
Class Mammalia

It is recommended to learn all of them, two fatures and atleast one or two examples. I know you wanted a brief one, but this is as brief as it gets!!
Hope u find this helpful!!