What is Pentecost?  This is a very special time in the Bible when the disciples and other Christians received the Holy Spirit. It is recognised as a 'birthday for the church' and was the start of us being able to ask for forgiveness.
Pentecost occurred 50 days after Easter Sunday or 50 days after Jesus rose from the dead.  Jesus had already gone back to Heaven so the disciples and new believers of Jesus were waiting to receive the Holy Spirit because that's what Jesus told them would happen.  Also, since Jesus wasn't with them any more the Holy Spirit would help bring them closer to God.
Just before Jesus was taken up to heaven he told them that they would receive power when the Holy Spirit comes on them and they'd be his witnesses in the whole world (Acts 1:8).  Even more, he told them much earlier that the counselor (or Holy Spirit) would be sent by the Father, that He would teach them all things and remind them of everything he said to them (John14:26).
So, the Holy Spirit is super helpful to us! He becomes a part of us when we become a Christian and understand that Jesus died and rose for us.  When we're ready to try to live a life pleasing to God the Holy Spirit becomes part of us so we have a part of God with us all the time.