Lower the payment
A lower rate on the same balance brings the payment down, and so does spreading what you owe over a longer run of payments, but those two are not the same thing. The second can cost you more in interest over the life of the loan while costing you less each month, which is why the calculator below prints both figures rather than only the flattering one.
Pay the loan off sooner
The opposite trade, and a deliberate one. Fewer years of payments means a higher payment each month and less interest in total. People do this when income has risen since they bought, or when retirement is close enough that owning the house outright matters more than the monthly figure does.
On a conventional loan on a one-unit home you live in, you may not need a refinance at all: the Homeowners Protection Act, subject to its conditions and exceptions, gives you the right to ask for borrower-paid mortgage insurance to be canceled once the loan is paid down far enough against the home's original value, and requires it to end automatically at a later point on the loan's amortization schedule. FHA is different: how long its annual premium runs depends on how much equity the loan started with, and moving to a conventional loan is one way out of it. Ask before you pay closing costs for it.
An adjustable loan holds an agreed rate for an opening period and then moves on a schedule tied to a published index plus a margin, with caps on how far it can travel. It suits somebody who does not expect to hold the loan long. Plans change, and when they do, refinancing into a loan whose rate does not move is how people buy the certainty back.
A home equity line of credit (HELOC) or a second loan sitting behind the first can be rolled into one loan with one payment and one payoff date. Worth checking carefully: a line of credit whose rate can move is not the same as a second mortgage at a settled rate, and consolidating them changes what the whole of your housing debt costs rather than only what it costs this month.
Take cash out
Borrow more than you currently owe and take the difference in cash. It is the one reason on this list that raises your balance instead of rearranging it, and the one that deserves the longest conversation.