Wher do Beta comes from?
Usually, when faced with a complicated system, it helps to find ways to simplify it, so that it's easily usable.

When we take a transistor connected in common emitter, and measure the base and collector currents, we notice a rough proportionality. It varies down a bit at very high currents, and very low currents. However, over several orders of magnitude, for reasonable currents like 1 uA to 10 mA (for small signal transistors) it's pretty close to constant. It's sufficiently constant that it's worth giving a name to, and it's called beta.