A Layer Break is the point at which you switch from the first layer of the disc (the first ~24GB) to the second. It isn’t usually a huge issue with blu-rays, since the players buffer so much video ahead of where you’re currently viewing. It’s a much bigger issue for dual layer DVDs. But to answer your question, it would be related to the burning procedure (software, settings) and to some degree the player. Not sure if the media itself can affect this, unless the player is struggling to read it and not buffering properly?
It’s worth getting decent discs at some point anyway. Blu-rays, unlike DVDs and CDs, have an extremely thin plastic surface to read through before hitting the data layer ( http://s.hswstatic.com/gif/blu-ray-6.gif ), meaning that a tiny, shallow scratch can hit the data. Official discs have very good protective, anti-scratch coating on the surface for this reason. Verbatim discs have a different, but still very good, anti scratch protection. I don’t know if other brands copy the technique or use their own, but I’d be wary to trust a cheap brand.
