Flash photography is a technique that uses artificial light to send out an intense pulse of light to illuminate the scene/subject. Flashes allow photographers to work in situations where the ambient light is insufficient. However, beyond just the ability to compensate for lack of light, flashes are also useful when overpowering mixed lighting scenarios.
Most modern digital cameras, barring a few high-end ones, come with built-in flashes. Beyond these, you can always invest in proper external flashes. These are more powerful than the built-in ones.
Beyond these, you have the strobes. Strobes are the most powerful, have the shortest recycle time and can be attached to AC mains or connected to portable power packs for extended usage. Flash units are synced with the camera to fire the optimum amount of light for proper exposure.
Most modern cameras use TTL metering and there are sync cables and electronic transceivers available which allow you to fire the optimum amount of light.