Voice lessons help you to learn the proper way to breathe and the right annunciations for certain syllables. Usually your instructor will give you pieces to study and work on.
Vocal improv is basically making it up as you go, but it has to be a part of the chord being played/sung by others. A great example of this is "scatting" in jazz music, or sometimes a cadenza. A more "toned-down" example would be experimenting with different rhythms or changing the melody a little bit in a song.