a bot is pretty much a piece of software that automatically makes your character perform certain actions in game, without requiring you to click anything or press any buttons. For example, in my signature i have a "WQ bot". When you run this program, it will detect what characters you have logged in, and if you select a character and press a certain button, the character will automatically pick up his world quest and fly to the next volume until its done.
In the meantime you can just go have breakfast, read a newspaper, go to work etcetera. And come back to see the bot is done with the quest. There are also bots for grinding experience, harvesting materials and things like that. A bot just makes you play the game while you are not there.