A combination of their nature, kinetic energy and size.
Alpha radiation is made up of helium nuclei. They are particles that are relatively large and therefore they are more likely to collide with other particles. They also have a large positive charge so they experience a large electrostatic interaction. For these reasons alpha particles have a low penetrating ability. Those alpha particles that have more kinetic energy will have a higher penetrating ability than other offer particles as they will require more collisions or interactions in order to stop them.
Beta radiation is made up of electrons or positrons. They are particles but they are small, they are therefore less likely to collide with other particles than alpha particles. They do have a charge (positive for positrons and negative for electrons) but it is smaller than for alpha particles, so they experience a moderate electrostatic interaction. For these reasons beta particles have a moderate penetrating ability. Like alpha particles beta particles that have more kinetic energy will have a higher penetrating ability than other beta particles.
Gamma radiation is made up of electromagnetic photons of very high frequency. They are extremely small, they are therefore extremely unlikely to interact with other particles. Gamma photons also do not have an electric charge, so they experience no electrostatic interactions. For these reasons gamma radiation has an extremely high penetrating ability.