In a decentralised market, the constant buying and selling of currency requires large reserves of many different currencies to facilitate individual trades. These reserves are created by users, who provide liquidity in return for a share of the transaction fees generated by the exchange, typically < 1% of each trade.
Users who decide to deposit their assets into these reserves (or liquidity pools) are called liquidity providers. They can choose how much or little of an asset they would like to deposit into the pool and receive a receipt for their deposit in the form of a liquidity provider (LP) token.
LP tokens, then, are a way for liquidity providers to prove their ownership of a certain share of the pool, and which can be redeemed for the originally deposited assets at any time.
Every transaction made within the pool is subject to a small fee, which goes directly to liquidity providers. The transaction fees are added to the pool itself, making it larger and more valuable, and increasing the value of the LP token as a result.
These fees vary based on the volume of trades in a pool and the amount of time the position is held. In all, LP token returns can be substantial for long-held LP tokens in pools with high trading volume.
As LP tokens are essentially a derivative asset, their value depends on the value of the underlying tokens. LP tokens representing a single-asset are generally very stable, however providing liquidity in paired-asset pools comes with the risk of higher volatility.
As with all derivatives, LP tokens of many established platforms such as Compound, Aave and Uniswap have their own secondary and tertiary markets with serious trading activity.
Further layers of financial offerings on top of such platforms are being built by projects like Yearn and Stake DAO, and staking the LP tokens themselves in a secondary pool can generate a high APY. This is an incentive mechanism used by protocols to encourage users in keeping their native asset liquid and is known as yield farming.