The Bergeron process is a mechanism that causes the formation of precipitations of many hydrometeors (rain, snow, hail, etc.).
The Bergeron effect is the continuous transfer of water vapour from supercooled droplets to ice crystals. This is due to the difference in relative humidity around the supercooled water and the ice: the humidity level is higher near the droplets than it is near the ice crystals.
Therefore water vapour diffuses towards the ice crystals, which become larger at the expense of the droplets. Their weight increases until it causes them to fall. A second phenomenon, coalescence, then comes into play to continue increasing the weight of the hydrometeors, leading to their precipitation.
The Bergeron process causes rain. © Iain Farquhar, Geograph CC by-sa 2.0