Holy Saturday is the day before Easter and after Good Friday. Churches that celebrate it reflect on the darkness of the world had Jesus never been resurrected. The events of the day before Jesus' resurrection are given in Matthew 27:62-66:
Holy Saturday - What is it?
The next day, that is, after the day of Preparation, the chief priests and the Pharisees gathered before Pilate and said, "Sir, we remember how that impostor said, while he was still alive, 'After three days I will rise.' Therefore order the tomb to be made secure until the third day, lest his disciples go and steal him away and tell the people, 'He has risen from the dead,' and the last fraud will be worse than the first." Pilate said to them, "You have a guard of soldiers. Go, make it as secure as you can." So they went and made the tomb secure by sealing the stone and setting a guard.
No reference is given to what Jesus' followers did on the day before His resurrection. It was the Sabbath, so they could not have travelled, and the women did not go to His tomb until the next morning.
As with the other extra-Easter festivities, Holy Saturday is mostly observed by Catholics and Anglicans. The "celebration" in the west is very austere, however. Sacraments are limited, often only given to the dying. Masses are rare. In Orthodox churches, the day is known as Holy and Great Saturday or Joyous Saturday. They believe this is the day that Christ released the saved from the Old Testament from hell and brought them to heaven (an unbiblical belief). Orthodox churches also call the day the Great Sabbath as it is the day Jesus rested in the tomb.
There is nothing wrong with celebrating Holy Saturday as such. It is fine to contemplate how the disciples must have felt—fearful, not knowing that their Savior would rise the next day. It is also fine to consider how dark our own world would be apart from Christ. Like Easter and the other "holy days" surrounding it, the Bible does not require that we do anything special. As Paul said in Romans 14:5, "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."
Holy Saturday Calendar
2018 – March 31
2019 – April 20
2020 – April 11
2021 – April 3
2022 – April 16
Palm Sunday - What is it?
Passion Week - What is it?
Maundy Thursday - What is it?
Good Friday - What is it?
Where was Jesus for the three days between His death and resurrection?
Truth about Christianity