Refinancing: taking out a new loan to replace a loan you already have for some sort of financial benefit
Equity: The value of the financed item minus what you still owe on the loan (for example, if a vehicle is valued at $15,000 and you have $5,000 left to pay on it, the equity is $10,000)
If you are halfway through your 30-year mortgage (meaning you have 15 years left of payments) but you want some cash so you can remodel and improve the value of your home, you can refinance your mortgage. You could take the equity in cash, which you could in turn use to purchase the improvements for the home. If the home is valued at $150,000 and you still owe $50,000, that means you could refinance it and theoretically receive up to $100,000 of cash back to use to improve the home.