Prevenient grace is grace that is extended to humankind in order that they may choose to follow God. Both Calvinism and Arminianism hold that man will not choose God on his own. Calvinism offers that God unconditionally elects people for salvation while Arminians claim that God offers prevenient grace in order that man may choose to follow God.
Prevenient grace is a conclusion that is drawn rather than a direct teaching of scripture. Because of their belief in free will Arminians reject the notion of irresistible grace and thus unconditional election. Scripture makes it clear that no one seeks God on their own. So prevenient grace is extended in order that man may have faith. This should be understood as a softening of the heart, allowing for free will to remain intact. It doesn’t “elect” or force anyone to become saved but rather opens the door for them so that they may choose whether or not to walk through the door on their own.