Refinancing means paying off your current mortgage with a brand-new one — new rate, new term, sometimes a new loan size. The house doesn't change; the debt attached to it does.
Borrowers refinance for three main reasons: to lower the interest rate (and the monthly payment), to change the term — say, trading a 30-year for a 15-year to pay the house off faster — or to pull cash out of home equity.
The catch is that a refinance is a full new loan, with its own closing costs and paperwork. The classic sanity check is the break-even point: divide the closing costs by your monthly savings to see how many months the new loan needs to pay for itself. If you might sell before then, refinancing loses money no matter how good the new rate looks.
For a walkthrough of when it makes sense — and when it quietly doesn't — see should I refinance.