What are the main differences between the Theravada, Mahayana and Vajrayana branches of Buddhism? The question basically says it all, but I'll try to elaborate a bit:

Are there differences in terms of the concepts used in each of these branches?
Are there differences in the practices of each of the branches?
Or are the differences between each of the branches simply explained in terms of historical or geographical factors?
This question, indeed, requires a whole book in order to be answered completely. Let me address only Theravada and Mahayana here.

In two words:


The most important aspect is that Theravada is focused on your own liberation from suffering, while Mahayana is targeted to all sentient creatures;
There are many consequences here:

Theravada assumes that you have to practice for yourself, while others can only suggest you. Mahayana says that you can (and have to) share your experience and accomplishments with others, thus making followers for yourself;
Theravada suggests to seek enlightenment for yourself first; Mahayana is up to delaying breaking off Samsara in order to help others;
Theravada practices are mostly silent and very personal while in Mahayana it is more often "wrapped" in some collective rituals like chanting;

In Theravada, the final goal for a Bodhisattva is nirvana. In Mahayana, prominence is important by itself;
Each teaching is more or less localized, e.g. at a certain country/territory there's usually only one;
If you'd like to read scriptures in original language, you should be aware that Theravada is written in Pali (Pali Cannon) while Mahayana is written in Sanskrit (Sutras);


Of course, there are also big differences in texts, ritual, etiquette, and so on.

This Comparative Study between two traditions provide with greater details.