Liquid staking is a variation on regular staking. Normally, when you stake crypto to help secure a network, those funds are locked and cannot be used elsewhere. Liquid staking aims to solve that by giving you a separate token that represents your staked position.
That token can then be used in other DeFi activities while the original stake keeps earning staking rewards. In effect, it tries to let the same value be productive in two places at once, which is why it has become popular.
The trade-off is added complexity and risk. The representative token depends on a protocol working correctly, its market price can drift from the underlying value, and stacking it into further DeFi adds more layers that can fail. This entry explains the concept; it is not a recommendation.