Liveness is the guarantee that a system will continue to provide data and that no central party can just shutdown their servers or censor data going to a smart contract.
For distributed systems, liveness means that a protocol is able to exchange messages among nodes, with the nodes successfully coming to a consensus. This means that a system has liveness guaranteed.
For example, Bitcoin's use of the Nakamoto Consensus means that there is an emphasis on liveness on Bitcoin's blockchain. Ethereum's Casper also guarantees liveness through its use of proof-of-work and block creation.