What is refinancing a mortgage?

Ok, I have told my mom that she should refinance her home for years. Now I realize that I know very little about refinancing.
What exactly are the details around a refinanced mortgage?

Friend of mine is a mortage loan officer. I've asked him about the topic a few times, even though I've yet to jump into the whole real estate thing.

A mortage refinance is when you take your loan and get it re-issued, usually at a lower payment, and then instead of having 30 years minus the number you've been paying so far, you have another 30 years to finish paying. But, the monthly payment is smaller. As an option, some people pull out a bit of equity, and then refinance at the same time, so that they have money in hand, and another 30 years to go to finish the payments, but the payments, if the house appreciated, are still lower than they were previously.

Hope that helps...if there are any real estate professionals in the crowd, I'm sure they can give you a better overview on things.