"Grace" as a word just denotes "gift." It is, in fact, what Advent is about -- a gift being given to humanity. The word "grace" shows up in "gratias" (for free) in Latin (which becomes gratis in UK/US parlance -- "no charge"), "gracias" in Spanish, and "grazie" in Italian. (The Romans used "gratis" for "thanks" in the same way that Spanish uses "de nada" -- "no problem/charge/burden" -- or English says "no big deal." Spanish and Italian derived their words from Latin.)“But a greater inconvenience it bred, that every later endeavoured to be certain degrees more removed from conformity with the Church of Rome, than the rest before had been; whereupon grew marvelous great dissimilitudes, and by reason thereof, jealousies, heartburnings, jars and discords among them” (Of the Laws of Ecclesiastical Polity I, 2.2).
Celebrating Christmas is strange. In a churchly setting, there is the mass of Christ -- the church service with eucharist/communion -- held to honor the feast of the birth of Jesus, but that is a single day of obligation. It doesn't necessitate, or bear, a great deal of wittering and frittering. On the other hand, Advent is the liturgical season leading up to the feast of Christ, and that does have pageantry and a series of themes. The traditional theme, and the one you will hear in your lectionary readings, is the fulfillment of prophecy, the kairos, or rightness and fullness of time.
The more Protestant side of the celebration is the theme of grace. Advent shows God giving a gift. Jesus's birth as man is neither obligatory nor deserved. It is something given by God for God's will. Man was dead set against the birth and the message.
Salvation had been possible before the incarnation, but only for the Chosen people, and only by the law. God gave a superabundant gift in being born and breaking the first major falling of man in the process. (When man fell, the first great consequence was being divorced from the presence of God. Being unable to speak directly to God and to know that there is a certain moral universe is the profound fall of the soul and undergirds all else.) God gave a second gift on top of that by giving salvation to any and all who would but follow the Christ. Men still had and have a choice, and they could -- as most did -- continue to insist that the messiah had to be a Davidic king who would conquer Rome and set up material wealth for Judea/Israel. Third, of course, in the death and resurrection, Jesus gave a gift of eternal life and the Kingdom of the spirit rather than the law. He sent thereafter the paraclete, or Holy Spirit. Since then, nothing has fundamentally changed or needed to change: through the comforter, we have access to God; we still must choose the Christ; gentiles and Jews alike are called.
This is grace. Man did not earn it. Man did not even know how to ask for it. What was given was given by God for God's will.
This is not how I hear people use the word "grace." I hear it, instead, used as "state of grace" and mumblejumble grace for salvation. I hear the word "grace" used to talk about a sort of rocket pack or Flubber for the soul. What's worse is that all of this comes out of the most perverse need to justify assumptions rather than observation.
One line goes like this: If men are born with a sin upon them, then men are born fit for Hell. If they are fit for Hell, then they are depraved. If they are depraved, then they are depraved through and through. If they are depraved through and through, then they can't choose to accept the Gospel and believe on their own. Instead, "grace" has to do it. Because grace, and grace alone, is responsible for the conversion of the depraved sinner to the saved elect, it is irresistible and total. What's more, it is "abounding" and "abiding," and that means that, having been the rocket pack that makes the person seek God, hear God, and accept God, it sticks around to steer.
The other line says, If men are born with sin upon them, then they are born erring. If they err by nature, they cannot see the good from the evil reliably. Their conscience now, their intellect then, and their bodies another time will alternately fail. Therefore, the seeker needs help -- a bit of extra bounce to get above human capacities -- but the seeker must then be peak human to decide on salvation. This grace is flubber, and it sticks around, too, but it is a special force that God brings to bear only when the human is in most danger of being lost.
The first of these theologies leads to abuses whereby people argue that their salvation is permanent, no matter what they do. As Fielding's Parson Adams says, they'll meet their Savior and say that, though they never acted on any of his commandments, they believed 'em all. The second one leads to further qualification and quantification of the types of human and supernatural flickering and sparking. Both lead to folks being the judge of their own grace and, if possible, other people's.
I lean far more toward the grace that resolves to the human soul's free will, but I mainly lean away from any discussion of "grace" as a thing. The arrogance involved in saying, from this example in the Bible or that one, that God affects a turning heart by doing exactly this for each and every heart is staggering. What Job went through is not what Mary went through, and what Peter went through is not what Thomas went through. For people to argue what "must" be the case with God's operation in the Holy Spirit is shocking.
We should, instead, be ashamed that we don't know how to respond to a gift. It is with gratitude and celebration.