Voicing
A voicing is the particular way a chord's notes are arranged when you play it: which note is lowest, which octave each note sits in, and whether any notes are doubled. One chord can be voiced in countless ways, and they all remain the same chord.
Take an E major triad - E, G♯, B. Played low to high as E-G♯-B, that is a plain voicing with the root on the bottom. Play it E-B-G♯ instead and it is still an E major triad, just voiced differently, with the third now on top. On guitar the same chord might come out E-B-E-G♯-B-E, where E appears in three octaves and B twice - again, the same chord, a fuller voicing.
Voicing versus inversion
These two ideas are close but distinct. A voicing is any arrangement of a chord's notes. An inversion is the specific case where the lowest note is not the root. So every inversion is a voicing, but as long as the root stays in the bass you can spread the upper notes however you like and the chord is not considered inverted. Choosing voicings well is how you control the texture and weight of a chord, and how you keep the movement between chords smooth.