Now, why am I not surprised that someone who has been around so long when encountering a new phrase, is too intellectually lazy as to not want to Google the thing?... Ok I'll humor you.
Hypostatic union (from the Greek: ὑπόστασις, {"[h]upostasis"}, "hypostasis", sediment, foundation, substance, or subsistence) is a technical term in Christian theology employed in mainstream Christology to describe the union of Christ's humanity and divinity in one hypostasis.[3]
http://en.wikipedia.org/wiki/Hypostatic_union (I normally don't trust Wikipedia, but this is such common knowledge...)
So in your Christian theology you never heard that Christ was both fully man and fully God? Hmmm.... Perhaps you don't believe that.
Why of course we can trust it. It's the fallible interpretations of humans that cause the problem. That's why Church history is so important.
WM