Private devotions are various things people do by themselves that help draw them closer to God.
Examples of private devotions are: praying the rosary, praying the Stations of the Cross, praying a novena for an intention that you have, kneeling in adoration before the tabernacle, reading and meditating on Scripture, etc.
Private devotions can be done any time of the day, and any day of the year, and as frequently as the person would like to do it.
I hope this helps answer your questions.