Because the Lord’s Day (Sunday) sanctifies and defines all other days of the week, and because Eastertide (a kind of “Lord’s Day” for the liturgical year) becomes an annual observance, it was inevitable that a special week would come to be observed in an annual cycle.  Of course, the most logical week to be regarded as holy is that week (known as “Holy Week”) which annually transitions from Lent to Easter day.
Palm Sunday (named for the palms used to welcome Jesus at his entry into Jerusalem) is also known as Passion Sunday [referring to Jesus’ impending suffering (from patior, Latin for “to suffer”)].  The basic reason is this: To separate out the narratives of the entry of Jesus into Jerusalem and interpret the occasion behind them as utterly joyous and victorious is to misread the Gospels.
During Holy Week, most Christians do not usually gather for worship until Thursday.  The three intervening days (known as Holy Monday, Holy Tuesday, and Holy Wednesday) serve primarily as times for personal contemplation.
Holy Thursday is more commonly known as Maundy Thursday [referring to the commandment or mandate (from mandatum, Latin for “command”)].  This day of Holy Week is a time to remember Jesus’ command to his disciples to “love one another.”  On this day, Christians customarily observe Jesus’ last supper with his disciples, and they often observe the rite of “Tenebrae” (from Latin meaning “darkness”)—a rite wherein lights are extinguished one by one as a symbol of the gloom of Christ’s death.
Holy Friday is more commonly known as Good Friday (a corruption of the English phrase God’s Friday).  It is God’s Friday precisely because God was in control at Calvary.  The crucifixion of Jesus was not some bad deal which God had to make the best of.  Rather, it was a working out of divine intention with a view to the salvation of an otherwise doomed creation.
Holy Saturday is marked the observance of the Great Vigil of Easter.  By its design, the Vigil recapitulates Lenten themes as it provides the final transition into Easter.