This is an evolutionary term describing a state in which an organism's body size or body structure becomes overspecialized such that it becomes a disadvantage. For example, overly large body size, or color/markings such that camouflage is no longer possible. Also, many traits which arise from sex selection tend to be disadvantageous overall to the organism (in terms of survival) but advantageous when the organism wants to attract a mate. Examples of the latter in modern birds would be a cardinal's attractive (but highly visible to predators) red color and a peacock's beautiful but unwieldy tail.
One of the more spectacular examples of hypertely was found in the now-extinct Irish Giant deer. The females' sexual selection of the bucks was based on their antler size. As a result, the bucks evolved enormous racks -- their antlers extended horizontally for up to 12 feet with huge spiked lobes at each end and could weigh over 80 pounds. Their antlers got so ornate and heavy that they became a serious liability to the species, and the deer died out.
Some of the information in this writeup was taken from the science dictionary at http://biotech.icmb.utexas.edu/; I oversaw the development of the dictionary (the website was mothballed in 1998) and I believe I wrote the entry this is based on.