Why is December 24th called "Christmas Eve"?
In old times, days started at sunset, so the evening of the day, the "eve" happened first. Then we changed to days starting at midnight. So now the "eve" is evening of the previous day. So "Christmas Eve" is the day before Christmas.

Where does the word "Christmas" come from?
Christmas = Christ - Mass = "The Mass of Christ"
Christ = Jesus Christ
"Mass" = Roman Catholic religious Church service of "mass".
The word "mass" probably comes from the last words of the service of "mass", which are "you are dismissed" = "missa est" in Latin.
From the Latin word "missa" comes the English word "mass"