A blast chamber is a chamber used to greatly decrease both the chance of item loss and the blast resistance of blocks while trying to break blocks with explosions.
It is important to note that this method only works with blocks that can be moved by pistons, and more importantly, most explosions can cause blocks and their items to be destroyed entirely, making it impossible to get them back. The exception to this are TNT blasts, where they drop all blocks broken as items as of Java Edition 1.14.
Principle
Blocks cannot just exist outside the block grid. However pistons appear to do this all the time. Actually, the blocks to be pushed are deleted, then moving piston are placed at the destination, then play the animation of blocks moving to give a sense of blocks moving.
This block has some interesting properties. It has a blast resistance of 0, and can't be broken by tools, but it can be broken by explosion, after that it will drop the same things the block it replaces would drop if broken by explosions, however with a 100% chance. Thus, blowing up a moving block greatly increase efficiency.
To get enough explosions for a blast chamber, either use TNT duplication, creepers, ghast fireballs, wither skulls or ender crystals, etc.
Since 19w11a, the usefulness of blast chamber is largely reduced - items destroyed by TNT now always drop regardless of movement. Motion still reduces blast resistance of blocks though,[1] so the classic blast chamber design yields more blocks broken per TNT. It may also be still beneficial with other explosion sources - Withers, Ghasts etc.