Chemistry is the study of the composition of matter and the changes that matter undergoes. Matter is that which has mass and occupies space. Chemistry involves both the living and non-living things since both are made of matter.
Organic chemistry is the study of compounds containing carbon. There are far more carbon-containing compounds than any other type. Since living things are made primarily of carbon-containing compounds, organic chemistry is often called the chemistry of life.
Biochemistry is the specific study of chemical processes in living things, so it's very closely related to organic chemistry.
Inorganic chemistry is the study on compounds that don't contain carbon. It involves a more general look at chemical bonding, chemical reactions, and chemical properties.
Physical chemistry mostly deals with energy changes that go along with changes in matter.
Analytical chemistry involves making measurements of substances and determining exact composition.