At the time of the Roman arrival, the Brigantes were the tribe that controlled the biggest contiguous territory among all of the Celtic tribes of Britain. "Brigantia" was a swathe of Northern England, reaching into the Midlands, centred on modern Yorkshire.
There is some discussion around whether their name was derived the Celtic root for the highest mother-goddess, Brigandu "the exalted one - often rendered in modern language as "Brigid", or whether it was toponymically derived from the tribe's occupation of hilly ground, cf. the German -berg suffix. Veneration of Brigandu was central to contemporary Celtic culture across Europe, and we see tribes using this name throughout Europe, and hills are good places for forts. I think it's both, and the two theories are unlikely to have been separable in the minds of the Brigantes themselves. The high places belong to the high goddess.
The Brigantes initially accepted the Romans and aligned themselves with the new force. The famous Brigantii queen Cartimandua handed over the rebel leader Caratacus, a fellow Celt of the Catuvellauni tribe. This led to her losing the favour of her own people, her divorce and abdication. She fled to the Roman lines, leading to a battle between the Brigantes under her former husband, Venutius and her Roman protectors around 50AD.
Cartimandua's abdication led to the Brigantes becoming an openly rebellious tribe at a time when Rome was itself politically unstable. The Brigantes continued to harass and put pressure on the Romans at least up until the mid-2nd Century AD, and probably were a factor in the construction of the Hadrian and Antonine Walls, to prevent the Brigantes from linking up easily with the Pictish tribes in Scotland. In 138AD the Brigantes staged what may have been their last major revolt, as Roman troops pushed north from Hadrian's Wall to where the Antonine Wall would eventually be built. The revolt was put down decisively, and the Brigantii's territory was garrisoned and fortified more heavily, but my understanding is that they were never conclusively subdued.
The Brigantii have been discussed as a possible cause of the disappearance of the lost Legio IX Hispana, which had been stationed at Eboracum. I'm currently working on a novel that features the Brigantii and the Ninth, but includes a very different explanation for the latter's disappearance.