The server downloads the page into its memory, and then displays it to the user.
From the point-of-view (in the technical sense) of the host hosting the target site, only the server visited.
This means only the server's IP will be logged, and not the user's (Ref: wikipedia)
What does "free web proxy" or "web proxy server" or "web proxy" mean?
In computer networks, a proxy server is a server (a computer system or an application program) that acts as an intermediary for requests from clients seeking resources from other servers. A client connects to the proxy server, requesting some service, such as a file, connection, web page, or other resource, available from a different server. The proxy server evaluates the request according to its filtering rules. For example, it may filter traffic by IP address or protocol. If the request is validated by the filter, the proxy provides the resource by connecting to the relevant server and requesting the service on behalf of the client. A proxy server may optionally alter the client's request or the server's response, and sometimes it may serve the request without contacting the specified server. In this case, it 'caches' responses from the remote server, and returns subsequent requests for the same content directly. (Wikipedia)