If you think of a crystal as being a tiny bell, it's easy to see how, if you hit it with a tiny little hammer, it would ring with a pure tone just like a big bell would if you hit the big bell with a small hammer.
That's exactly what a crystal does, but the trick is that it's made of piezoelectric material which makes electricity when you hit it and changes shape when you shock it with electricity.
To make it produce that pure bell-like tone continuously, it's connected across an amplifier which works just like someone pushing you on a swing so that when you got to just a little past the peak of one swing they'd give you a push to make sure you came back for the next one.
The piezoelectric nature of the crystal causes it to change shape when the amplifier output "pushes" it with an electric signal, and then when the amplifier lets go, the crystal springs back and generates its own signal which says "push me", and sends it to the input of the amplifier at just the right time for the amplifier to generate another push and regenerate the cycle, forever.
So what makes the crystal start oscillating?
There's noise everywhere, and it's like zillions of tiny hammers hitting everything all the time.
Some of that noise hits the crystal, and when it's hooked up to the amplifier and starts to ring a little from the noise hits, the amplifier gets the electrical signal from the crystal's physical ringing tone (frequency), builds it up, and sends it back to the crystal. That makes the crystal change shape even more, sending a bigger signal back to the amplifier when the crystal's shape springs back, until the system is oscillating continuously and is stable.