Ok you now see how it works but there is another thing that happens with solenoids when they get many hours of use as they carry high current. The tips inside will become worn and not able to carry the current required by the starter. It's probably unlikely but it does happen. Some solenoids have a flat contact bar which connects the two big terminals and some have a round disc contact that connects the two large posts. As those contact tips wear they dont transfer power well. You could see 12 volts travel across the contacts or you could see a connection with your ohm meter but if worn they may not carry current to the starter.
A solenoid is a device that lets a little guy (small wires) tell a big guy (heavy cables) what to do. If you ever get ahold of an old solenoid break it apart and it all becomes very clear.