The 1k resistors are a sort of "wired OR" between the arduino digital pins and the USB serial pins.
If you've connected D0/D1 to logic gates that are operating in 0/+5V, the 1k resistors allow those signals to "swamp" the signal from the USB chip, so it works. If they weren't there, the USB might drive +5V (during idle times) while the external device was driving 0V, and that would be ... not good. The 1k resistors have nothing to do with impedance matching.