What we know of the Pictish presence in what is now Scotland does not suggest that they tended toward collecting in large population centers; settlements—if any—around royal forts were the norm. If there were a capital city for the Picts, however, this was it.
Carbon dating shows the main walls constructed perhaps as early as the 3rd century, but additional layers of walls were added over time. A Late Bronze Age spearhead and a coin from Nero's time suggest that the place may have been used earlier and taken over by Picts: its location on a promontory made it easily defensible. It fell out of use after the time of the Viking raids.
It would have taken a lot of effort to conquer: the walls were eight meters thick and six meters high. Oak logs were nailed together with 8" iron spikes to make a framework which was then filled with stone and rubble. The construction makes clear that whomever wanted it built had access to a very large workforce.
It was geographically at the center of the Pictish Kingdom of Fortriu. It seems that Fortriu was the most powerful of the Pictish kingdoms, and Burghead was likely the seat of its kings. Early records sometimes refer to Fotriu as if it encompassed all of Pictland, suggesting its prominence. Adomnán's Life of Columba describes the fort of a Pictish king as being situated where Burghead is. Bede describes the same king as rex potentissimus or "very powerful king," further suggesting that whomever ruled Burghead was more powerful than other Pictish kings.
In the 19th century, its remains were dismantled for their materials. About 30 stone panels carved with images of bulls were noted before being incorporated into the quay walls of the harbor. The handful remaining above water are in museums and the Burghead Visitor Center.*
...which I guess is as good a segue as any to Pictish art and artifacts, for which you'll have to check this space tomorrow.
*Their website has an outline of one of the carved bulls on its main page.