How are innovation and revolution linked together?

The term revolution is fairly ambiguous and can refer to anything from a single person revolting against a small group to a large body of people revolting against their government. Assuming that you're referring to a political or national revolution, the strongest link is related to need or desire.

Broadly speaking, a population revolts when they feel that their governing body is no longer acting on their behalf or adhering to their wishes. For example,...

The term revolution is fairly ambiguous and can refer to anything from a single person revolting against a small group to a large body of people revolting against their government. Assuming that you're referring to a political or national revolution, the strongest link is related to need or desire.

Broadly speaking, a population revolts when they feel that their governing body is no longer acting on their behalf or adhering to their wishes. For example, the American Revolution was largely the result of the colonists feeling as though the British government wasn't representing their interests and didn't really care what they wanted. As a result, they ultimately waged a war against the British in order to take control of their territory and become a sovereign nation. In this case, the colonists had a need (many needs, actually) that were going unmet, so they had no other choice but to create a governmental system that worked for them.

As for innovation, an innovative idea, product, or service usually comes into existence out of need. The computer, for example, was once a giant machine that took up an entire room of a building. They were expensive, highly complex, and generally unwieldy, which meant that, despite their potential, the ordinary person couldn't use one and probably wouldn't want one. Given that, several people started to think about ways that the computer could be made smaller, cheaper, and easier to use, constantly refining their ideas and designs eventually leading to the cell phones, tablets,and laptops that we use today.

In both cases, there is an obvious desire or need for something that doesn't exist. Yet, rather than be content with what did exist, the people took it upon themselves to get rid of the dysfunctional or broken thing and create something new that would meet their needs.