Let's say you want to figure out if the user clicked/touched the left or right side of the window, and that your window is 800 units wide. Then the code is very simple; in your click handler (typically love.mousepressed()) check if the x position of the mouse is less than or greater than half that, 400:
function love.mousepressed(x, y, button, istouch)
if button == 1 then
if x < 400 then
-- left side clicked
else
-- right side clicked
end
end
end
But if you're doing anything more complex than that, like a GUI, this quickly becomes unmaintainable. Think about adjusting those GUI elements, adding new buttons, resizing them, changing the layout, and calculating those magic numbers... yuck! Then it's best to look at a proper GUI library, or code your own. But under the hood the library will be doing the same thing - checking the mouse press against coordinate numbers.