Mammals, Fish, Birds etc are Classes of living things within the Vertebrate Division of the Animal Kingdom. Insects fall into one of the Classes of living things within the Invertebrate Division of the Animal Kingdom.
Until the middle of the 20th century living things were divided into two �kingdoms� � Animals and Plants. With new scientific discoveries it was realised that this was not sufficient as many organisms did not fit readily into either of the main groups. Constant debate has been ongoing concerning the classification. The most accepted model at present consists of five Kingdoms � Animals, Plants, Bacteria, Fungi and Protoctista. This last Kingdom encompasses mainly Protozoa and Algae, but is used for convenience for anything which does not readily fit the other four, which have clear definitions.
The full classification �tree� below Kingdom is: Division; Class; Order; Family; Genus; and Species. A handy mnemonic for this which I was taught at school is �King David Come Out For God�s Sake�.
Many living things are known by a combination of Genus and Species (e.g. Homo Sapiens for humans). The full classification �tree� for humans is Animal (Kingdom), Vertebrate (Division), Mammal (Class), Primate (Order), Homididae (Family), Homo (Genus), Sapiens (Species).