The LP token is a receipt with maths attached. Holding 1% of the supply entitles you to 1% of whatever the pool contains at the moment you exit, in whatever ratio the pool happens to hold then, plus your share of accumulated fees.
Because it is a normal token, it can be used elsewhere: staked in a liquidity-mining program, posted as collateral in a lending-protocol, or wrapped by a vault-strategy that compounds the fees. Each extra layer adds contract risk on top of the pool's own.
Valuing an LP token requires care, and getting it wrong has been costly. Naively pricing one as reserves divided by supply lets an attacker unbalance the pool and misprice the token, which is a recurring form of oracle-manipulation. Note also that newer concentrated-liquidity positions are issued as NFTs rather than fungible LP tokens.
Related: liquidity-pool, impermanent-loss, liquidity-mining, vault-strategy