I thought roseway might have been right: H = Gain.
In electronics, the gain of a transistor is usually written a h
FE; a very common parameter.
When you look in detail, it might not be quite so obvious:
Etymology of hFE shows that this term is actually one of many
"h-parameters" ... and they aren't all gain.
In other places, the channel characteristics seem to call "H" the "Transfer Function", which seems to be a mathematical model to represent the output vs input of a black box (in this case a length of copper pair)
Wikipedia's page on Transfer Functions shows H(s) defined as a transfer function.
I guess in this case, the transfer function does indeed represent gain (or loss).
JDSU seem to call it
Transfer Function too.
Edit: Fix URL & typo for transistor