Also called adjustable or floating rate.
A loan with a variable interest rate will see it fluctuate over time as the underlying asset moves up or down. The same premise holds true for securities with variable rates.
The advantage is if the underlying asset suffers a decline, the interest rate will decrease. Naturally, the disadvantage is the opposite is also true. This will affect the amount paid on the loan (or return on the investment).
How often this rate will change is up to the lender. A common form of this is a Home Equity Line of Credit (HELOC).