Note, I am a software guy, if somebody who is a EE replies with a different answer, believe them.
Unless you cut the trace, VIN and VUSB are connected together. So if you apply power to the VIN pin, it can be fed back to the USB connection if the VIN power is higher than the USB power. Some USB connections aren't prepared if you feed power back to them.
If you cut the trace, then you must apply power to the VIN/Ground. The Teensy will not work if you just plug in the USB plug without applying power to the VIN pin. Note, the USB connection will not be used to power the Teensy.
One use of cutting the the trace is to connect a lipo battery charger to VUSB and ground. Then you connect the power output from the charger to VIN on the Teensy (connect ground to both). If they charger has a battery connected, but no USB, then the battery will power the Teensy. Depending on the charger, if you connect a USB cable, the Teensy will either be powered by the battery or straight from the USB connection, and the battery will be re-charged from the USB power source.
Another use is to provide an on/off switch to the Teensy, where you connect an on/off switch between VIN and VUSB.