F.J. Sheed did an excellent job in explaining the mystery of the Holy Trinity in his book Theology for Beginners:this blog post. The Trinity, since it is a mystery, is extremely hard to explain without accidentally falling into various heresies that have been rejected by the Church; even I mess things up, so for the time being I'd rather leave this in the hands of the experts!
There's a great story involving St. Augustine. He was strolling along the shoreline, contemplating the Trinity, when he spotted a small boy who had dug a hole in the sand and was trying to scoop up water from the sea and dump it in the hole. St. Augustine asked the boy what he was doing and the boy said, "I'm trying to put the sea into this hole." St. Augustine said, "But you'll never be able to do that!" The boy said, "And you'll never be able to fully understand the Trinity..." and he disappeared. It remains an incredible mystery of the faith.