LED Driver Sink Current
The current value depends on the led requirement, you should drive the leds with the proper current to have the desired luminosity, the device you are talking about actually can change this current to have different luminosity levels. The 60mA of the device is the maximum the device can lead. They talk about sinking current because the led are connected to the VCC and the device "ground" the LED to switch it on, so the current flows inside the LED and "sink" into the device.