A forex robot is a piece of automated forex trading software that automates trading decisions. The most popular robots for retail traders are built around the Metatrader platform. These robots run on metatrader as "expert advisers" and they can do anything from giving you a signal to place a trade, to placing and managing the trade for you automatically.
If you have a forex strategy that is strictly mechanical and doesn't require a human in the decision making process, you can program your own forex robot to trade for you 24 hours a day.
There are many companies out there that create and sell forex robots. If you're in the market to buy one, be careful who you deal with. It's common for a company to spring up overnight and start selling an "instant riches" forex robot, including a money back guarantee, only to disappear in about 45 days or so.
The majority of forex robots out there are not profitable. If you are planning on purchasing one, please do your research.