What is Equity Swap?

Legal Definition
An equity swap is a financial derivative contract (a swap) where a set of future cash flows are agreed to be exchanged between two counterparties at set dates in the future. The two cash flows are usually referred to as "legs" of the swap; one of these "legs" is usually pegged to a floating rate such as LIBOR. This leg is also commonly referred to as the "floating leg". The other leg of the swap is based on the performance of either a share of stock or a stock market index. This leg is commonly referred to as the "equity leg". Most equity swaps involve a floating leg vs. an equity leg, although some exist with two equity legs.

An equity swap involves a notional principal, a specified duration and predetermined payment intervals. The term "tenor" may refer either to the duration or the coupon frequency.

Equity swaps are typically traded by Delta One trading desks.
-- Wikipedia
Legal Definition
Actual trading full or partial ownership of one or more security vehicles or investment risks between one or more parties.