The ‘short and meaty definition’ of grace, I believe, is this one I found somewhere:
Grace is unconditional acceptance [by God] given to an undeserving person [the sinner] by an unobligated giver [God] (Emphasis mine).
This short-on-word-but-long-meaning definition has three parts; unconditional acceptance, the undeserving person, and the unobligated giver.
Romans 5:8, “But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.” God’s love for us is not conditional. Like I will accept you if you make this standard, no. Because “while we were yet sinners”—He took us in no matter our badness.
This unconditional acceptance comes to an undeserving people. We are sinners. We are bad people. We do the nastiest things that can be done under the son—we are undeserving considering that God is holy—this however does not stop His acceptance of us. Our underserving nature makes claim solid for God’s unconditional acceptance.
We have to notice that God is under no obligation to accept us—He is God. But he does. This is the grace we are talking about. It’s the love of God to us (which we never return anyway!). “For God so loved the world.” This is God’s so great love.
That we are accepted unconditionally in our badness by a God who is under no obligation to accept us but then goes ahead to accept us anyway!