To be restive is to be impatient or on edge — it's an edgy state. When you feel like your skin is too tight and your nerves are ready to snap, when you feel ready to explode, you are restive.
It's not only people who can be restive: the world suffers from much turmoil, and there are restive areas, where people are unhappy or oppressed and desperate for change. It's that need for change and movement that makes someone restive or eager to move, frustrated at being stuck in one place. This sense of being stuck is obvious in the history of the word, which was first used in the 15th century. It evolved from the Anglo-French adjective restif, which meant "refusing to move ahead." Picture a restive horse, refusing to take a jump.