When we announced our friend from Matera that we are planing to visit his town early June he said...nooooooo, please come in July you need to be there on the 2nd of July to take part in Festa della Bruna... so now I can share with you what it is all about.
We arrived in Matera close to midnight the day before the celebration. The city center was packed with people and everywhere you had a lot of decoration. At a point everyone stopped to admire the lights dancing on famous Italian music
"The Festa della Bruna (Festa di Maria Santissima della Bruna, Festa della Madonna della Bruna) is the principal festival of the town of Matera, in Italy's southern Basilicata region. Although the festival is in honour of the town's sacred protectress, the Madonna della Bruna, it is far from being a purely religious event. Tens of thousands of local people turn out onto the streets for a week of celebrations with coloured lights, market stalls, town bands and grand processions. Events climax with a pagan-style rite of destruction, before a valedictory firework display." (Source)
If you are from the region the day itself could have more meaning, but as a tourist I must say that I could not figure out a lot what was happening. It was so so so full of people. If you are interested in all the details you can check out the event's page.
If you are into fireworks, the show is spectacular so make sure to get a good spot to see them. These are fired up from the Belvedere.
Keep in mind t: if you stay in the center there will be canon shooting as of the early morning...just not to get scared :). It's an interesting event which is worth experiencing if you are in/around Matera in that period.