I put some pictures of the last reading I did up on my website (including the one above). It was a musical written around the music of Peter Gabriel called US. These types of events happen all the time in NYC. It's a chance for writers, composers, etc to see their work performed without having to put up a ton of money for sets, costumes, a venue, etc. Most of these works are "a work in progress", so there are many changes to come. This was the first public performance of US. It's great for we actor folk because you meet a lot of new people in a short amount of time (a reading usually only take 1 week to rehearse and is only 1 performance). Plus, you have to think on your feet and learn the show VERY quickly. An added bonus is discovering great new music like Peter Gabriel's. I really had no idea of the depth of his work. You should check out some of his stuff from the late 1980s to early 1990s.
Tarzan started like this. In fact, I think there were several "readings" before they moved forward with a full production. Even from the first rehearsals, there were many changes before we finally opened on Broadway. There are actually lots of different things in the German production too. It's fascinating to see how art progresses.

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