In short, Blu-Play is a term used by the homebrew community of game-developers to categorise "Small-scale homebrew games for your PlayStation 3, PlayStation 4 and Xbox One game console", using a technology that makes it possible to run the same disc on all 3 consoles - without doing any hacking or modding whatsoever.
In contrast to big expensive mainstream full-blown 3D games released by the big game-companies, Blu-Play games will always be much smaller cosy 2D games developed by a single individual, or a small group of enthusiastic hobbyists.
Blu-Play games will mostly be completely free to download and play, but there may also be developers who'll ask for a fair price for their games.
The technology used to create Blu-Play games has been around since 2003. It's called Blu-ray Disc Java, often referred to as JavaME BD-J. All Blu-ray players run BD-J as part of the Blu-ray specification, which in turn means that PS3, PS4 and XB1 all run Java games simply because they all feature a Blu-ray player. The whole idea with BD-J was exactly to offer games (among other things) on Blu-ray players.
In other words: Your console was designed for this!
The short version: You download the ISO, burn it to disc, and pop the disc into the disc drive of your console.
The longer version is here.