Rooted in Gestalt theory and print/editorial design conventions — not one person's invention, but a long-standing graphic-design practice. The eye lands, in order, on the largest element, then bold, then high-saturation, then whatever is surrounded by whitespace.
In practice, designers rank every element on a screen as 1st, 2nd, or 3rd priority, then scale size, weight, colour and spacing to match that rank. Five buttons in the same size and colour leave users unsure which one to press (see: call-to-action).
The numbered badges below appear in the actual order the eye is drawn — biggest and boldest first.
When to use
Whenever a screen mixes three or more pieces of information, rank them first, then differentiate size, weight and colour. "Everything is important" usually means "nothing has hierarchy."