The word as used in the scriptures, refers primarily to the divine help and strength we receive through the Atonement of the Lord Jesus Christ. The Apostle Peter taught that we should “grow in grace, and in the knowledge of our Lord and Saviour Jesus Christ” (2 Peter 3:18).
A regular dictionary defines the religious aspect of grace as
a : unmerited divine assistance given humans for their regeneration or sanctification
a) correlates that we are receiving divine help. I often feel that I do not merit the Atonement's power in my life. But my Savior loves me. He loves each of us. And the Atonement was made for all.
What I also love from the quote I found, it refers to the scripture about growing in grace. I think on that and I get two things from that.
1) When we use grace, or the Atonement's enabling power, we are enabling ourselves to grow more in every aspect of life, especially to grow more like Christ.
2) The enabling power itself can grow in our lives. It isn't just one level or size of power to access. The more we use it, the greater, the stronger, and the deeper it affects our lives and our efforts to live righteously and work toward returning to Heavenly Father.