Definition
An exit node is the last hop before traffic leaves a privacy network and enters the public internet. In a single-hop VPN, the VPN server itself is the exit. In a Tor circuit, the exit relay is the third and final relay before the destination website sees the request. In a multi-hop VPN, the exit is the second (or third) VPN server. The exit node's IP is what the destination logs as the visitor.
Trust Model
The exit node has a privileged position: it sees the unencrypted contents of the request (assuming the request itself is not separately encrypted, e.g., via HTTPS) and the destination. Tor exit nodes are run by volunteers, some of whom are known to log or modify traffic; HTTPS protects the content but not the destination domain. VPN exit nodes are run by the provider, which is why provider trust matters: the entire model rests on the provider not abusing the position.
Why You Care
The exit IP is what determines geographic appearance — connecting to a US exit makes services see you as a US user. It also determines reputation: if the exit IP has been blacklisted by a streaming service or website (because of past abuse from any user), you inherit that block until you switch exits.