Logging into a website with Facebook/Twitter/Google etc.

Please excuse my ignorance, but I really don't understand this concept.

I have been to 100's of sites and most of the sites I access show me an option to log in with the details I registered my account with, but also have a log in with Facebook or Twitter option.  

I have never actually ever logged into any of these using Facebook or Twitter because I don't know why I would want to. I am considering learning how to do this but am also asking myself why I would want to do this and what is the benefit?

If someone could please explain it to me I would be most grateful. I know I can just ask Google but a lot of times Google gives me way too much info and can end up being more confusing that informative.

Thanks