A phototransistor is a switch that is triggered by light. A transistor is a device that allows electric current to pass through it if its gate or collector is supplied with an electric current. A phototransistor on the other hand allows electric current to pass through it if it is exposed to light. Depending on the model, this could be visible light or infrared (IR) light.
The most well-known type of phototransistor is the infrared type found in remote-controlled appliances such as TVs. The simple light-triggered functionality offered by phototransistors has made them quite useful for a number of applications. For example: A phototransistor can be used to determine the ambient light level and adjust the brightness of your monitor or phone screen for maximum visibility out in the sun, battery life, or minimal eye strain if its dark.
A phototransistor can also be used to transmit signals. A TV remote, for example flashes an infrared LED many times in a certain sequence if you press a button. The phototransistor (or similar device) in the TV will then allow electricity to pulsate through it in the same sequence that the remote did, and then that sequence of electrical pulses is translated into instructions (for example: the instruction to switch to channel 4).
A series of phototransistors could also be used to determine the position of the sun for a solar tracker, or to determine if its dusk so that your outside lights can be turned on.