In the UK, summer music festivals are famous for being rained on and the whole event turning into a mud bath. Also summer concerts are an essential part of growing up, so much so that people still go to them when they're in their 50's and 60's.
Putting up with a concert that becomes a mud bath is considered to be a initiation ceremony into adulthood. A formative experience that binds friendships, starts romances and is remembered with affection and laughter, "Do you remember Susie falling over in the mud at Glasto. LOL that was so funny" and so on, for years afterwards.
See Glastonbury 2016 mud bath and Glastonbury Festival backgrounder
Glastonbury is so big it's broadcast live on BBC national TV see BBC Glasto 2016 and all the national papers have daily commentaries on the acts along with pictures. But there are lots of other similar festivals throughout the summer, with equally unreliable weather.
Hence the phrase "a free concert in the mud—plays an outsize role in shaping a group of young people" would be understood by anyone living in the UK.
You usually have to pay though, so the 'free' part of 'free concert in the mud' is misleading.