Sinking and sourcing are terms used to describe how a load (the device being turned on or off) is powered in regards to the sensor.
Sinking is the most common and it involves the switching of load current (power) supplied by a power source external to the sensor. With this configuration, current passes through the load first, through the output switch of the sensor second and finally to ground. Sensors with sinking output switches the negative leg of the circuit.
Sourcing refers to a configuration in which the sensor is the source of the current required to power the load. In a sourcing situation, current supplied by the sensor passes through the load second and then to ground. Sensors with sourcing output switches the positive leg of the circuit.