While the existing answers are not wrong, I think there are a few distinctions worth mentioning. An example may help:
Consider a box. Inside the box, there is a red hat, a yellow hat, and a blue hat (and nothing else). Each of the following is an accurate and correct statement about this situation:
The box contains a red hat and a blue hat.
The contents of the box include a red hat and a blue hat.
The contents of the box consist of a red hat, a blue hat, and a yellow hat.
It would grammatically correct, but inaccurate, to say:
The contents of the box consist of a red hat and a blue hat.
This is because (as Jasper points out), 'consist' is used for an exhaustive description of a set.
The distinction between 'includes' and 'contains' is a bit more subtle. 'Contains' is used when there is something else that is doing the containing. The box is a container, and contains the hats. You would not, generally, say that the box includes the hats. Inside the box is a set of objects, and that set (which 'contents' refers to) includes (and consists of) the hats.
'Includes' is also often used when talking about the features of a product or thing for sale. If I were selling you the box, I might tell you that it includes three hats. In this case, I'm not pointing out that the hats are inside the box, but rather that the box and the hats are all part of the set of things I'm offering to sell.