First of all, many of the Jewish feasts have direct Christian counterparts, because the Law was perfected and fulfilled, not totally abolished. There’s a very good series of talks on salvationhistory.com about this, called Feasts of Faith; and you can also notice this by close reading of the Gospels. Here are some examples:
Passover/Pascha = Easter
Shavuot/Feast of Weeks = Pentecost
Sukkot/Feast of Tabernacles = Transfiguration
Secondly, it was always the Jewish custom that great days in the history of the Jewish people be celebrated as feasts or fasts. Some of these are recorded in the Jewish Bible, others are recorded in the Catholic Bible (as the origin of Hanukkah is recorded in 1 and 2 Maccabees), some are recorded in the Old and New Testament as having been celebrated, but aren’t mandated anywhere Biblical.
It was also usual among Jews to remember great holy people or martyrs for God on the anniversary of their deaths (as well as one’s own loved ones).
When the earliest Jewish Christians began to have great holy events occur, or had martyrs die for God in impressive ways, they simply continued to do the same things they would have done when they were Jews: they remembered these great events and great deaths on the same day every year. Some of them made it into the New Testament, and some of them didn’t, but everybody took note of the important days. (And so did the pagan Roman government, as they were always catching Christians who were doing grave visits to martyrs’ graves or celebrating Christian holy days.)
The main thing that keeps people from seeing this continuity is that we use a solar calendar, whereas the Jewish calendar is lunar/solar. But it’s not a secret. So yeah, if you look up the traditional holy day for St. Samuel, it’s the same day that Jews used to celebrate the prophet Samuel’s holy death. Not a big secret.
All of history and every day belongs to God. Setting apart certain days to remember God’s goodness and celebrate those who have been faithful is a good way of remembering that “this is the day that the Lord has made; let us rejoice and be glad in it.”