A bot which is short for a robot is a type of software application or script that performs automated tasks on command from a centralized command and control center (often called as the mother ship)
They are specialized piece of malware that lie dormant until and unless they receive command from a mother ship.
Once the computer gets affected with this malware, your computer becomes a bot, and since there is no malicios activity visible, it can go undetected for a lifetime. The compromised machine is then referred to as a zombie.
A single bot on its own can't be of much use. So, the attackers trick the victims to install these bots on as much computers as possible. This army of bots is called a botnet.
Botnets can be used to implement a DDos Attack, to render a service or a network unavailable.The attacker can even rent the botnets to clients (for a particular period of time) for appreciable amount of money.
More the number of bots that get installed on computers, more is the strength with which an attack can be launched.
For example: A bot takes 1Mbps of bandwidth. Then an army of 1000000 bots can take up a bandwidth of 100Gbps ( 1Mbps * 1000000) which is more enough to bring down a simple website.