The corners reflect which modifier key(s) you use to get that symbol or function.
Bottom/Left: No modifier
Top/Left: Shift
Symbols on the bottom/right and top/right are accessed through the Alt Graph key (many European layouts) or in a special mode (that's how IBM's Japanese layouts work, if I understand it right).
In European layouts:
Bottom/Right: Alt Graph
Top/Right: Shift + Alt Graph
Keys with legends that are centred vertically do not take modifiers. This includes the modifier keys themselves, Enter, Caps Lock etc.
The Tab key is a special case, in that the textual legend "Tab" (when present) is centred vertically but the symbols for
Tab and
Back-Tab are at the bottom/left and top/left respectively.
Then there are keyboards that break the convention for stylistic reasons ... or because the designer is dumb and does not understand it. (Which is why there is a "↹" symbol in Unicode
)
Then there are Japanese conventions that put glyphs not in corners but left (centred vertically), top (centred horizontally), etc.
However, I believe that the origin of the convention started not from thoughtful design but as a stylistic choice for the DEC LK-201 terminal keyboard where most legends were adjusted to the top/left. The DEC terminals were very influential at the time. For instance, the LK-201 also introduced the inverted-T cursor key layout and nav cluster in-between the main and numeric clusters -- which IBM copied for the Model M keyboard.
The LK-201 did actually have spherical key tops. Why most keyboards since the Model F have had cylindrical key tops is because they copied IBM and because manufacturers went from expensive double-shot moulding to various forms of printing and it is much easier to print on cylindrical keys.