The Uber Nature is one of the things that are unique to Pokémon Omega.
Each Pokémon you catch or obtain has a nature. Natures are a crucial part for a Pokémon's potential in battle. Most increase a stat by 10% and decrease another by 10%.
The Uber nature, however, only increases the Attack stat by 10%, and decreases nothing! This is very useful for a Pokémon that you would normally want a +10% Attack nature for, since Uber does not decrease a stat, giving it a little advantage over the same Pokémeon with, for example, the Adamant nature.
Uber Natured Pokémon can be obtained in any way other than catching them yourself. (Note: natures don't change through trade, so you can only obtain Uber natured Pokémon through trade if they already were Uber) This includes Events, Premium Boxes, Fossils, Starters, Quests where the Pokémon's nature isn't set, and evolving Nincada, which creates the chance for Shedinja to be Uber. (note: Ninjask's nature will be the same as Nincada's)
Since the Uber nature can only be obtained through those ways, it is rarer than Pokémon with other natures. In some cases, those Pokémon are more valuable for collectors. This is with Fossils, Starters, Shedinja (to some, even though it's still just a map Pokémon) etc. Pokémon that the Uber nature is beneficial to, are also more valuable. For Pokémon that it's of no use for, and don't belong to the above categories, are not worth any more than any other pokémon with a +10% Attack nature.