There are a lot of beliefs and ideas that float around about what/who the Holy spirit is. This can cause a lot of confusion in people's minds about who/what is the Holy spirit's purpose.
I believe Jesus said it best of what the Holy Spirit is and His/Its purpose in John 14:26: "But the Comforter,
which is the Holy Ghost (remember this!), whom the Father will send in my name, he shall teach you all things, and
bring all things to your remembrance, whatsoever I have said unto you."
Just a few verses prior (the whole chapter, really), Jesus is comforting those who are following Him as Jesus is sharing His future departure, ensuring that they continue to do the things He has commanded/said to them.
In short, the Holy Spirit will bring back to our memory the things Jesus said. That is the purpose. The Words of the Lord Jesus the Christ.
Why did Jesus send the Holy Spirit to the disciples on the day of Pentecost?
That was not the first time the disciples received the Holy Spirit though. Again, in the Gospel of John, Jesus said, "Then said Jesus to them again, Peace
be unto you:
as my Father hath sent me, even so send I you. And when he had said this, he breathed on
them, and saith unto them, Receive ye the Holy Ghost: Whose soever sins ye remit, they are remitted unto them;
and whose soever
sins ye retain, they are retained." - John 20:21-23.
Though, to answer your question, I believe Jesus sent the Holy Spirit on Pentacost for the purpose of transmitting a message to many people of many nations.
The book of Acts opens up with, "The former treatise have I made, O Theophilus, of all that Jesus began
both to do and teach. Until the day in which he was taken up, after that he
through the Holy Ghost had given commandments unto the apostles (again, see John 14) whom he had chosen: To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and
speaking of the things pertaining to the kingdom of God. - Acts 1:1-3
Continuing on in Acts 2:5-6 And there were dwelling at Jerusalem Jews, devout men
, out of every nation under heaven. Now when this was noised abroad, the multitude came together, and were confounded, because that
every man heard them speak in his own language.
And finally the result of this is in verse 41, "Then they that
gladly received his word were baptized: and the same day there were added
unto them about
three thousand souls. (Praise God!!!)
The reason Jesus sent the Holy Spirit at Pentacost is because it is what He instructed His disciples to do to show He (Jesus) was true in what He said. Like Jesus said in Matthew 28:19-20, "Go ye therefore, and
teach all nations,
baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway,
even unto the end of the world. Amen."
Which is what happened at the end of Acts 2:42 And they continued stedfastly in the apostles' doctrine and fellowship, and in breaking of bread, and in prayers.
Though, Marks Gospel account goes into a bit more detail of what Jesus said was to come; reflecting EXACTLY what happened at Pentacost. "And he said unto them, Go ye into all the world, and preach the gospel to every creature. He that believeth and is baptized shall be saved; but he that believeth not shall be damned. And these signs shall follow them that believe; In my name shall they cast out devils;
they shall speak with new tongues. - Mark16:15-17
Pentacost is a recorded account showing that what Jesus said is absolutely true! With that account being evident, it brings to question; what else did Jesus say throughout His 3 year ministry that is also true?
In peace and Love