Aqueducts were the most famous way the Romans used arches, but they really used arches in all their buildings. With an arch, you could build a big room, without having to find huge trees to make the roof out of. Just small stones would do, or even just clay for bricks.
If you want to see how this works, first observe how arches are built. You could look at a real arch near you, or a good picture of an arch in a book or on the internet.
At the Exploratorium in San Francisco
Now try taking wooden blocks and building an arch with them. You can use a U-shaped prop to hold it up while you build it, and then take the prop away to see if it stands up. Or, build your arch lying down on a board, and then see if you can tip the board up and keep the arch standing. (Hint: for the keystone, you may need a trapezoidal block).