Prevenient grace is grace of God that comes before to a person that enables him or her to be able to choose God. It is not based upon anything in and because of that individual. Theologically speaking it is a position held by Arminians and not by the Reformed. Prevenient Grace is necessary only when a person's natural sinful condition will not freely allow him to believe. So, Arminians do acknowledge the doctrine of total depravity otherwise prevenient grace would not be a necessity.
Prevenient grace does not regenerate the person, but it is supposed to re-enable the individual to be able to freely choose God. It is a type of freeing from the bondage of his sinful nature. This grace can be successfully resisted by the sinner.
So, prevenient grace refers to the grace that precedes a person's decision to believe in Jesus. In other words, it is the grace that God provides for a person that enables the person to freely choose God.