This term is short for Robot. It refers to a software program that is designed to read web pages without a human controlling it. Every search engine company has a software program to read and save web pages. These search engine "bots" are usually called spiders and it's their job to find all the pages on your website.
There are other types of bots too. In my experience none of them are good. Unless you're a search engine performing a service, there is no other reason to use a bot program other than information theft. There are "email bots" which will read website looking for email addresses. There are "virus bots" that will scan the internet looking for websites to deface. There are "screen scraping bots" that will copy all your information and republish it on their own website.
Please stay away from anyone talking about a bot if they are NOT referring to a search engine. They are probably involved with some shameful practices.