In the Bible, the word holy means “set apart.” God is holy. Christians are called to be holy. A holy day, then, is a day that is set apart to focus on the things of the Lord. There are holy days mentioned in the Bible, and, over the centuries, Christian churches have instituted other holy days by tradition.
The Bible mentions at least eight holy days (or groups of days), also known as feasts or festivals. They are Passover, Unleavened Bread, First Fruits, Pentecost/Weeks, Trumpets, Tabernacles/Booths, Purim, and the Day of Atonement. Of those eight, seven are commanded in the Mosaic Law (Purim was a later development). These Jewish/Old Covenant holy days are not mandated for followers of Jesus Christ, but they can be observed as a remembrance of how Jesus perfectly fulfilled them.
Over the centuries, various Christian churches have instituted holy days (or groups of days). The two most common are Christmas and Easter. Other commonly observed Christian holy days include Lent, Palm Sunday, Maundy Thursday, Good Friday, Pentecost, and Advent.
The New Covenant does not advocate the observance of any Christian holy days, but neither does it forbid such observance. Romans 14:5 appears to be the guiding principle: “One person esteems one day as better than another, while another esteems all days alike. Each one should be fully convinced in his own mind.” If a Christian is going to observe a holy day, he/she should be fully convinced that it does not violate God’s Word, that it can be done to the glory of God (1 Corinthians 10:31), and that it would be spiritually beneficial (1 Corinthians 6:12; 10:23).
Ultimately, for the follower of Jesus Christ, every day should be a holy day. Every day of our lives should be set apart to worship God, obey His Word, and live a holy life. That is likely why the New Testament does not advocate specific holy days. Perhaps a good way to put it would be, “For the Christian, there are seven holy days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.”