Of these three terms, science is the broadest, biology is one kind of science, and anatomy can be seen as a part of biology.
Science just refers to all attempts to study the world using the scientific method. That is, science is the attempt to learn about the world by forming hypotheses that can be tested. This is as opposed to fields like philosophy or history where theories cannot truly be tested and "falsified."
Biology is the science of life. Anatomy is clearly part of biology, but anatomy looks only at the structure of living organisms. By contrast, biology can look at the processes that go on within cells (Krebs cycle, for example) or at the interactions between all organisms in an environment (ecology).
Science is a very broad term. It consists of observing, identifying, describing, investigating, and explaining any kind of phenomena about the world that can occur. As you can see, this is very broad and can consist of many different things.
Biology is the study of life. It is more specific than science but still a fairly broad term. Biology is limited to the study of living organisms including structure, function, origin, evolution, etc.
Anatomy is more specific and concentrates on the structures of different living things. For example, there is plant anatomy, human anatomy, or the anatomy of any other kind of organism.