At its most basic, a heartbeat is just a regular communication (which can be either push or pull) with a node in a distributed system in order to prove that it is still healthy and functional.
Xu (p. 102) discusses a for Gossip protocol for leaderless distributed systems in which each node disseminates its heartbeats to a random set of neighbors, as well as disseminating updated heartbeat lists for all the nodes whose heartbeats they have seen. If some threshold number of nodes report that they have not become aware of a heartbeat from node