The important thing about a phenomenon that nobody has mentioned is that it is something that is newly and somewhat suddenly popular. Something that has been popular for a long time is not a phenomenon. It may have been when it first became popular, but it is not one any more.

something considered fabulous or catchy around the world.

The phrase 'worldwide phenomenon' is used to say that something (in this case, brass bands) is popular in places all across the world. Basically, this is saying that there are many countries all across the world that listen to brass bands, that might play in brass bands, or that brass bands may just be well known in many other countries.

Yes that’s what it means. The second definition of phenomenon in OED is a remarkable person or thing. And when worldwide is added it means popular around the world.