A 2-pin crystal is basically like a tuning fork. If you bang it on something it will ring at a specific frequency, but die away eventually. You can make an oscillator out of a tuning fork by putting a microphone on one side, and a speaker on the other. Just like a PA system will squeal due to feedback if the microphone is next to the speaker, this system will oscillate. Unlike the undisciplined feedback of the PA system, it only works at a single frequency very close to the natural frequency of the tuning fork.
A 4 pin crystal oscillator has essentially this circuit built in. There is a little amplifier that amplifies the output from one terminal of the crystal and applies it to the other. All of the components are set correctly so that you apply power and you get a clock out.