Voicing a chord refers to bringing out the various notes it contains. Sometimes we want certain notes to ring out (resolutions, etc.) and other to float in the background. Doing this can make a huge difference in your interpretation and overall sound.
Take, for example, this common voicing of an A minor chord:
To bring out the top voice (the high A), first play it alone. Get that note in your ear. Then play the entire chord while applying slightly more pressure to the a finger. You should hear that high A ring out above the rest of the chord. This method can be used for the rest of the voices in this chord as well.
Voicing chords different ways can bring different things into your ear. Experiment with it in your pieces and see what pops out. It’s really amazing how much a chord’s sound can change just by bringing out a different voice.