No Cash-Out Refinance
  
A large share of mortgage refinancing takes place so the homeowner can withdraw some of their equity. Basically, the person owning the home wants to use it as a source of cash.
You bought a $500,000 house 15 years ago. You put $100,000 down and got a 30-year mortgage for the remaining $400,000, with an interest rate of 7%. Now it's 15 years later and you've accumulated $150,000 in equity in the home. A typical refinancing might see you take out that $150,000. You'd get a new 30-year loan, covering the entire $400,000 borrowed against the house. You'd get a check for $150,000 (minus any fees), and now you have 30 years left to pay off the new loan.
A no cash-out refinance doesn't involve taking out the $150,000. The main reason to conduct this form of deal is to take advantage of lower rates.
Rates have fallen over the past decade and a half, and now you can get a mortgage with a 5.5% rate. Your original mortgage has 15 years left to run with a 7% rate...with $250,000 in principal remaining. You'd save money getting your rate down to 5.5%. So you run a no cash-out refinance. You get a 15-year mortgage for the $250,000 left remaining, with a new interest rate of 5.5%. You original bank gets paid back and you end up with lower monthly payments. And you still only have 15 years left on the loan.