Ah .. shall we say you are opening up a can of worms for a forum discussion? There is not a simple one sentence answer. Voice leading is a lesson or more, all in its own, based on the principles of harmony, chord structure, and scales.
However, here is a brief (although not comprehensive answer):
If I played an open C major chord on the 1st, 2nd and 3rd strings (only) on the guitar, I would be playing an E, C and G note respectively. If I changed that chord to an F chord, I would be fretting the 1st and 2nd strings at the 1st fret and the third string at the 2nd fret. I now am playing two new notes (E and A) and one common note (C). The notes of the F chord are F, C and A in order.
Both the C and F chords have a common note C. Two of the pitches (notes) of the C were raised to get to an F. The highest voice in C (the E note) was raised to an F. The lowest voice in the C chord (the G note) was raised to A. The C note was common and didn't change.
Instead of thinking of two separate chords, we maintain or retain the common tones and move in semi-tone or tonal increments the uncommon notes.
Confused yet? Good, because the next discussion would be about parallel movement, contrary movement, similar movement and counterpoint.