What do we mean by honest nodes? In his recent paper, Vitalik often mentions the term "honest nodes". What do we mean by that exactly?
An honest node is a node that does not try to modify history. This is opposed to an attacker node which tries to modify a past block in the blockchain presumably to benefit them financially.

Note that because transactions are cryptographically signed, "An attacker can only try to change one of his own transactions to take back money he recently spent," Bitcoin Whitepaper.