I know PPP is used for point-to-point connections. The Wikipedia article for "point-to-point" says that the term is used to refer to a wire that links only two computers or networks, as opposed to, say, a crossbar or bus that links several. The Wikipedia article for PPP states that the protocol is used to establish a "direct connection" between two nodes on a network. I am concluding from this that PPP is used only to establish a connection from one node to the next immediate neighbor; it is not concerned with sending traffic down multiple routers. It establishes communications between two hosts that are adjacent to each other on the network, with no other hosts in between, or with the illusion that there are no other hosts in between (in the case of, e.g. VPN). Am I right in thinking this? I'm kind of confused here, because terms phrases "direct connection" and "links only two computers" are kind of vague. If I am wrong in my interpretation of these phrases, then can you explain what they are supposed to mean?
PPP is an extensible encapsulation-protocol which operates over a DTE/DCE connection. This implies two endpoints (one DTE and one DCE). These endpoints are adjacent to each other over the real or virtual circuit.
Cisco has a PPP description document: Point-to-Point Protocol
PPP is a layer 2 protocol, and like most layer 2 protocols, it is usually dependent on the physical media. The Wikipedia article you quote lists the kinds of media normally used with PPP.
In other words, you choose the L2 protocol based on the communications media, not on who you're trying to communicate with.