Question about Consensus

Hi there, I'm currently learning all about Bitcoins functionality for a school paper.

However I can't quite grasp the concept of consensus, probably because I don't understand the definition.

I understand consensus as the general agreement over the whole network, e.g. about the validity of a transaction.

A sends a Transaction to B. A signs the transaction with a valid digital signature and the transaction gets broadcastet to each node. Each node now independently verifies this transaction and propagates it to their neighbours. Is this verification process also part of consensus or not, because I only seem to hear about consensus in the context of proof of work and mining verification.

I thought that consensus is reached through cryptography and that consensus replaces the need for a central authority, also in the verification of independent transactions and not only blocks.

Any clearing up and help would be greatly appreciated!