The general meaning of "margin" isn't to convey "move this over by 10px" but rather, "there must be 10px of empty space beside this element."
I've always found this is easiest to conceptualize with paragraphs.
If you just gave paragraphs margin-top: 10px
and had no margins on any other elements, a series of paragraphs would be spaced beautifully. But of course, you'd run into trouble when placing another element underneath a paragraph. The two would touch.
If margins didn't collapse, you'd hesitate to add margin-bottom: 10px
to your previous code, because then any pair of paragraphs would get spaced 20px apart, while paragraphs would separate from other elements by only 10px.
So margins collapse. By adding top and bottom margins of 10px you're saying, "I don't care what margin rules any other elements have. I demand at least 10px of padding above and below each of my paragraphs."