Equivalent means something has the same value or is interchangeable. For instance, $1 is equivalent to 100 cents, four quarters, 10 dimes or 20 nickels. Likewise, 60 seconds is one minute, 365 days is a year and 5,280 feet is the equivalent of 1 mile.
When talking about two sets, equivalent means both sets have a one-to-one correspondence, meaning one part of a set is paired with a part of the other set. Equivalent shapes in geometry have the same angles, area or volume. A square with sides of 2 feet in length is equivalent to a second square with each side of the same length.