Holy Ghost, Batman

A theological plea today. I understand why the need is there to differentiate between God and Jesus, but what exactly is the Holy Ghost and what does it do that cannot be folded into the Father or the Son? When someone "feels the Spirit", why wouldn't this be a feeling of connectedness with the Father or Son or both? Is the Holy Spirit like school spirit in that way, only made into a metaphysical entity like a Platonic Form? Could someone clearly explain the theological role of the Holy Ghost and why the Trinity has to be a trinity?