The alpha particles leave visible tracks in the cloud chamber because

Answer: Ionization

The inner atmosphere of a cloud chamber is composed of an easily ionizable gas, this means that little energy is required to extract an electron from an atom. This gas is maintained in the supercooling state, so that a minimum disturbance is enough to condense it in the same way as the water is frozen.

Then, when a charged particle with enough energy interacts with this gas, it ionizes it.

This is how alpha particles are able to ionize some atoms of the gas contained inside the chamber when they cross the cloud chamber.

These ionized atoms increase the surface tension of the gas around it allowing it to immediately congregate and condense, making it easily distinguishable inside the chamber like a small cloud. In this way, it is perfectly observable the path the individual particles have traveled, simply by observing the cloud traces left in the condensed gas.