an antenna with the bandwidth ratio larger than 10:1 for impedance bandwidth 10 dB return loss is called super wide band (SWB) antenna. there is also extremely wideband antenna (greater than 26:1)
It was approved IEEE Standard P1672 "ULTRAWIDEBAND RADAR STANDARD 1672 TERMS AND DEFINITIONS " Prepared by the Ultrawideband Radar Working Group of the of the IEEE Aerospace and Electronic Systems Society. Please, look. There are these and many other definitions here.
The bandwidth in terms of impedance is depend upon the except-able limit of impedance or SWR. e. g. For 1kw power radiation, obvious requirement is SWR should be about 1.1:1 or better. If you are using less power (order of mW or W ) the exceptable limit could be 1.5:1 SWR. This means return loss could be as hogh as 21 dB in former case and about 10 dB in later case.
Thus, the frequency band is based on the application. The super band antenna is wide band antenna or frequency independent antenna. There are varieties of antenna in this category e. g. Log spiral, log periodic, self complementary etc
The term super bandwidth is relative, it depends on the materials of the antenna, size, and the technology used. Other requirements such as power, efficiency plays an important role in determining the impedance bandwidth on the antenna. Well to me the term "super bandwidth" is application specific.