On the piano it means you play the quarter note with one hand while the other rests before it continues playing its part (in this case, the same cleff).
I've seen it for guitar too - often when fingerpicking. Means the same thing. The bottom note shows the bass line - often played with the R H thumb. While the RH fingers play on the higher strings. It means the bass line makes a quarter note rest. (assuming you're right handed).