Pentecost is one of those days in the church year that tells us exactly when it will occur. The name comes from Greek referring to the 50th Day. Pentecost is, in fact, 50 days after Easter.
Pentecost marks the end of the Easter Season, and reminds us of the Holy Spirit coming to the Disciples. This is shortly after Jesus' 40 days appearing with the Disciples post-resurrection, as discussed at the start of Acts.
The Day of Pentecost is also a reminder of what comes after, mainly the Disciples' spreading the Good News of the Resurrected Lord to all they encountered in the world. It is a reminder that we are called to carry out the same work now in the world.