For further info here is the informative Wiki article:- https://en.wikipedia.org/wiki/Eisteddfod (with 20 language versions at present)
There are a huge number held throughout Wales, from village ones up to the two national ones, at the end of May for young people, and the begining of August for every age group.
The key to this cultural phenomenon is that all competition is in Welsh.
There is also an international one in Llangollen.
The Eisteddfod tradition has been taken around the world by emigrant Welsh people and some still continue to thrive, most noteably the Sydney one, although in this case the link to Welsh has more or less vanished. https://sydneyeisteddfod.com.au/
The 2016 National Eisteddfod is being held in Abergavenny, 29 July - 6 August, within a few minutes walk of the train and bus stations. There is always a 'Maes D', which is where activities particularly aimed at Welsh learners are held. You do not need to be a fluent Welsh speaker to enjoy the Eisteddfod, though, and any of the main events which are Welsh-language only are likely to have simultaneous translations available through headsets
We have an Eisteddfod here in Tilehurst, Reading, UK. Growing up in the mid nighties, it was a sort of inter-school arts’ competition but a quick google search tells me it is now mostly a dance competition.
I had no idea what Eisteddfod meant when I was little but you don’t question stuff like that.