People building houses or any other kind of people have always had this one big problem, which you may have had also if you ever tried to build a clubhouse: how do you get the roof to stay up?
How do you build the part of the wall over the door or the window? One way (the way people figured out first) is to have a long piece of wood or stone that goes over the whole way from one wall to the other, like this:
But if you want to make a big building, you need very long beams to make a flat roof like that. And there are not very many big trees in the Mediterranean, so it is very hard to get so many long beams. One thing that helps is to make slanted roofs (gabled roofs), which is what most Greek temples have. But you still need a lot of expensive long beams.
The arch is a way of making a roof or a doorway or a window without using any beams at all: just a lot of small stones, or small blocks of wood, or clay bricks. That's a lot cheaper and easier to get than the big beams. You use the weight of the blocks to hold the arch together.
You can try this yourself if you get a set of arch-building blocks. Or cut them yourself out of wood. Try it with Legos. You lay the arch out on a board laid flat on the floor, and then tilt it up slowly and see if it holds.
Eyewitness: Building, by Philip Wilkinson, Dave King, and Geoff Dann (2000). Lavishly illustrated, like other Eyewitness books for kids, and with good explanations of most architectural terms.