Well tomorrow is Christmas Eve, so today we will explore the Etymology of the word Christmas. Yesterday we looked at the Etymology of the word Holiday that stands for Holy Day. Now on to Christmas! The following is from etymonline.com about the word Christmas:

"Christmas (n.)
"Church festival observed annually in memory of the birth of Christ," late Old English Cristes mæsse, from Christ (and retaining the original vowel sound) + mass (n.2).

Written as one word from mid-14c. As a verb, "to celebrate Christmas," from 1590s. Father Christmas is attested in a carol attributed to Richard Smart, Rector of Plymtree (Devon) from 1435-77. Christmas-tree in the modern sense is attested by 1835 in American English, rendering German Weihnachtsbaum. Christmas cards were first designed in 1843, popular by 1860s; the phrase Christmas-card was in use by 1850. Christmas present is from 1769. Christmas Eve is Middle English Cristenmesse Even (c. 1300)."

We have another perspective presented to us from celebratingholidays.com:

"The Name Christmas

By the Middle Ages, Christians were celebrating the remarkable event of Jesus’ birth with an extended season that began with Advent (four Sundays before Christmas) and continued for the 12 Days after Christmas (up until Epiphany on January 6th). The time preceding Christmas used to be a solemn time of fasting, whereas the days after Christmas were the time of celebration. Christians looked forward to the Midnight Mass of Christmas Eve with great anticipation, because it was the service that marked the transition from fasting to feasting. This service, known as “Christ’s Mass,” eventually became a description for celebrations of Jesus’ birth throughout the world. The word Christmas has its origin from the old English term Cristes Maesse, meaning “Christ’s Mass.”1

Though the word Christ is commonly used as Jesus’ name, it is actually a title. It comes from a Greek word that means “Anointed One” (the Hebrew word is “Messiah” — a term that Old Testament prophets used to describe the coming Savior). It should be noted that the abbreviated term Xmas does not necessarily take the “Christ” out of Christmas. The first letter of the Greek word for Christ (Χριστός) is “X” (pronounced “kai” in Greek), and it has been used throughout history to represent Jesus’ title.

The word Mass comes from the Latin word missa, which means “dismissal.” During the Middle Ages, the term became a general description for the Eucharistic service (the bread and wine of which Christians partook in remembrance of the body and blood of Jesus).2 The word gives insight into how medieval Christians understood at least one of the significant aspects of the Eucharist — they gathered together to remember the body (and great sacrifice of Christ), so that they would be strengthened to go (or more specifically, be “dismissed”) back into the world to BE he body of Christ. The apostle Paul told of this mystery when he wrote to believers in Corinth, “Now you are the body of Christ, and each of you is a part of it” (1 Corinthians 12:27)."

Finally we have this definition of the work Christmas from gotquestions.org:

"What is the origin of Christmas?

Christmas is a popular December holiday celebrated by large numbers of people all around the world. Christmas (or “the Mass of Christ”) has long been known as the celebration of the birth of Jesus Christ, and the celebration first began to be observed in the early fourth century. However, some traditions associated with Christmas actually began as a part of pagan culture; these were “Christianized” and given new meaning by the church.

The exact date of Jesus’ birth is unknown, as the Bible does not give specifics as to the dates of either His birth or conception. But in the second century AD, a Roman Christian historian named Sextus Julius Africanus calculated Jesus’ birthdate to be December 25 (nine months after Jesus was conceived, according to Africanus). In spite of the assumptions made in Africanus’s line of thinking, the date of December 25 was widely accepted.

At the time of Christ, Roman culture already celebrated a holiday in December: Saturnalia honored the god Saturn and was celebrated from December 17 to about December 24. Later, the Romans began celebrating Sol Invictus or the “Unconquered Sun,” associated with the winter solstice and observed on December 25. When Rome eventually instituted Christianity as the state religion in the fourth century, the Roman church converted Saturnalia and Sol Invictus to a Christian holiday, the Feast of the Nativity, in order to commemorate Jesus’ birth, thus providing a spiritually positive alternative to a pagan celebration. The sinful customs and debauchery associated with Saturnalia were “cleaned up,” and some of the customs were absorbed into the celebration of Christmas. Christians have “redeemed” December 25 and have celebrated it as the birth of Christ ever since the fourth century.

Given the association Christmas had with the ancient pagan calendar, the question then becomes, “Since Christmas shares a date with a pagan holiday, is it acceptable for Christians to celebrate it?” It is important to note that Christmas, Saturnalia, and Sol Invictus were all distinct holidays; they were never identical to each other. Also, although some elements of Christmas celebrations (e.g., bells, candles, holly, and yule decorations) are mentioned in the history of pagan worship, the use of such items in one’s home in no way indicates a return to paganism. Christians simply celebrate Christmas to remember the birth of our Lord and Savior, Jesus Christ. Celebrating Christmas is a matter of conscience (see Romans 14:5).
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So as you can see the common meaning is a celebration of the birth of Jesus Christ. Thou as pointed out in the last reference when this birth was it not known. As noted in this article the December dates were Pegan in nature to start and once Rome Converted to Christianity this become "Feast of the Nativity". After removing the Pegan aspects the calibration of the Birth of Jesus was set forth. Some of the customs we use today were Pegan at the start, but has been repurposed to Christianity. As noted, elements of Christmas celebrations (e.g., bells, candles, holly, and yule decorations) are mentioned in the history of pagan worship, the use of such items in one’s home in no way indicates a return to paganism. In fact for me as a Buddhist these are still lovely reminders of Jesus Christ and his teaching of wisdom and love. I still celebrate Christmas with the Christians because Jesus Christ was a very Enlighted bean that preached of love and forgiveness that even Buddhists also believe. Plus it is fun to give gifts to friends and family showing that you love them and care. Tomorrow on Christmas Eve we will look at Pets and Christmas! Some laughs are Awwww's coming to you tomorrow. Stay tuned!

Have a Merry Christmas!

References:
1. https://www.etymonline.com/search?page=1&q=christmas&type=
2. https://www.celebratingholidays.com/?page_id=996
3. https://www.gotquestions.org/Christmas-origin.html