And now I want to give up on understanding these things too...
The second Jersey link has a conversion clicky. Use that, and you're looking at both bulls with a US-proof. I get the impression there's some accuracy lost in a conversion, but at least you're not trying to compare an actual average with a deviation from breed average (or however the furrin place writes it out).
Daughters/herds/reliability - that's one of the first things to look at. 20 daughters/18 herds means you can use the numbers as a guide, but as more daughters are tested the numbers can change considerably. A first proof run in NZ is usually 70 2-yr olds completed their first lactation and gives a reliability of 80 - 85%, ancestry information only is about 30% and several hundred daughters with production records gives right up to 99% - meaning you can have faith in the numbers.
Some-one no doubt will correct me if I'm wrong on this - US dairy proofs are standard deviations within breed. So the average Jersey cow is 0 and the bull is expected to throw daughters that deviate +/- as indicated - so Kwartz is taller and stronger than average, higher volume with a slight negative on components and is expected to earn you $US517 dollars more than the average Jersey milking today... but with a reliability of 77% you needn't place any bets on him.
I'm making the presumption that the '0' value is a rolling (up-to-date) average. In both Britain (historically - I'm not up-to-date) and NZ we use a base year, and in NZ we're currently comparing bulls to cows born in 1995 (and across breeds, the comparisons aren't within breed for a NZ dairy proof).
On the USS Angus bull, note how the accuracy drops for maternal traits. The calving ease, birth weight etc can be measured nine months from using the sire, but maternal traits I'd guess are based on this bull's older female relatives, and take at least three years from first use to obtain from daughters.
We have this:
http://www.aeu.org.nz/page.cfm?id=15 which only applies to bulls with daughters tested in NZ.
Hmm - I just looked at that and I'd say it's next to useless for explaining. I'll need to try googling up some of those sites Dun mentions. Another source is the pdf-files of the actual catalogues the breeding companies send out - hidden away among the glossy pictures there's some times an explanation of what the various traits mean.