Most of what we know about the Druids comes from the Romans who wrote about them - the Druids existed between about 400BC & 400AD, primarily in the British Isle and also in Gaul (modern France). Early Roman writers (like Julius Caesar) seem to've been impressed by the Druids. They are described as playing extremely important roles in both the secular & religious life of their communities, they were highly organised & hierarchical and held gatherings where knowledge etc was passed between them and presumably some of it back out to their communities. The Druids themselves haven't left us much evidence because they adhered to an oral tradition for communicating their knowledge - the experts speculated that this might be partly for memory training, and partly for restricting the knowledge to those who were supposed to know it. The Romans were impressed with the philosophy of the Druids, and some later authors drew comparisons between Pythagorean ideas (I think about the soul) & Druidic ideas (which is pretty high praise for the Druids given how highly esteemed Greek philosophers were).
Many later Roman writers have a change in tone towards the Druids - much less favourable, and more inclined to see them as troublemakers. Perhaps because when you are conquering somewhere having an organised priesthood that has frequent countrywide meetings to exchange knowledge is effectively having a resistance movement. And the Druids had something to lose - the Romanisation of Gaul & Britain reduced their power & replaced them with Roman administrators and Roman religious temples & priests. Later still, Christianity played a part in stamping out the last remains of Druidic culture in Ireland & Wales even tho early on there was some coexistence between the two.
The respect of the Romans for the Druids is still obvious even in the later times when they are stamping them out. When the Romans went to march on the Isle of Anglesey one of the most holy Druidic sites they took on the order of 20,000 soldiers with them, which is rather a lot for an island populated largely by priests. This happened in the same time frame that Boudicca rose up to revolt against the Romans on the opposite side of the country, and the assault was abandoned to march back to deal with her army. Aldhouse-Green made the point that this is unlikely to be coincidence and she thought it was likely that Boudicca's revolt was timed to prevent the destruction of Anglesey - there is apparently some evidence that Boudicca herself was a Druid.
The programme then jumped to the 17th Century reinvention of Druidism - mostly lead by English clergy, it seems. It's from these people that we get the linkage between Stonehenge & Druidism - because knowledge of the true extent of the history of humans in the British Isles wasn't known in the 17th Century they assumed that anything pre-Roman pretty much happened at the same time. So Stonehenge is pre-Roman and Druids are what were there before the Romans, so therefore Druids built Stonehenge. Which isn't at all the case - Stonehenge pre-dates the Druids by a couple of thousand years! However, Cunliffe did suggest that perhaps the culture that built Stonehenge developed into the culture that had Druids, that there's some continuity there due to some similarities between archaeological evidence for religious practices in the two time frames.
In this segment of the programme they also touched on how the Bardic tradition in Wales & Ireland may've grown out of the Druidic culture - that it's the closest thing to continuity there is between actual Druids & what people in the 17th Century were trying to rediscover. And that that's not much continuity at all. But the Romantic reinvention of the past didn't just give us some colourful stories & myths, it also helped the development of archaeology itself - people bought up sites that were thought to be holy to the Druids to preserve them, and to investigate them.