Iron’s natural crystal structure (at room temperature) is called “body centered cubic”, or bcc (first photo). This is a cube with Iron atoms at each corner, and one in the very center of the cube.
When steel is heated up to critical temperature, AKA the point at which the metal will no longer stick to a magnet, the structure converts Austenite, which is the term for when heat changes the crystal structure to “face centered cubic” (fcc), which is when the cube has an iron atom at every corner, as before, but this time has an atom at each face of the cube, instead of one in the center.
How does this affect a blade? Austenite is essential for heat treating. When the Iron converts to Austenite, and retains a face centered cubic structure, there is room inside the cube for carbon atoms. The carbon, which had just been floating around each cube, now enters inside the cube. Depending on the rate of cooling, this can do several things. If the steel is cooled slowly, the carbon is able to come out from the steel easily as the Austenite converts back into bcc, and settles into a nice, relaxed pattern, making the steel soft and easy to form. If the steel is dunked in water or otherwise quickly cooled, the carbon does not have enough time to escape as the fcc converts to bcc, and so the carbon becomes trapped in a rigid, stressed way. This makes the steel extremely hard, but very brittle.