In the mathematical branch of graph theory, a node (or vertex, from Latin nodus, ‘knot’), is the fundamental unit of which graphs are formed. A graph consists of a set of nodes and a set of edges connecting them.
In computer science, nodes are devices on a network or data points on a data structure. On the Internet Protocol specifically, a node is any device with an IP address, which serves as identification and for location addressing.
In distributed systems, nodes are networked computers, which have the same goal for their work without a shared clock. They might have shared memory or operate under their own private memory.
A cryptocurrency network is a distributed network that reaches consensus on shared memory, the distributed ledger or blockchain. Any other device connected to the network is a node, such as lightweight wallets. The responsibilities of a “full node” are in fully validating transactions and blocks, enforcing the consensus rules. Most nodes also accept transactions and blocks from other full nodes, validating them, and relaying them further to other nodes.
Miners, which might or might not be required to be full nodes in the network, depending on the cryptocurrency protocol. In most implementations, including Bitcoin, miners only need to know about the prior block, while full nodes require the entire blockchain.
Nodes work all at once with little coordination. They do not need to be identified since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can leave and rejoin the network at will, accepting the proof-of-work chain as proof of what happened while they were gone.