If you wondered what affect aperture had on a photo then these two images should resolve it for you.

The first shot was taken at F1.8 (wide open). This means only a very small portion of the image will be in focus and depending on the quality of the lens, the background will me more or less beautifully blurred. You would use lower apertures like this for weddings/portraits and artistic shots where you want the viewers eye drawn to a specific subject.

The second shot was taken at F11 (closed way down) and gives a completely different feel. You would use an aperture like this for group photos or landscapes where you want every detail possible.

When you shoot with small point and shoot cameras they all have very high apertures which means almost everything is in focus. It is great for snapshots on vacation or at parties, but it's very difficult to produce artistic shots for framing. Not impossible, just more difficult.

As a general rule, the larger the sensor (and usually the camera too), the more depth of field you have to play with.

Lenses with very low apertures tend to be very large and very expensive. Consumer lenses start at about F3.5 whereas pro lenses go down to about F1.2. You also pay more because the expensive lenses tend to have more aperture blades that produce a better out of focus blur, also known as brokeh.

This photo ( https://pbase.com/bob_n/image/110231626) was taken at F1.8 and simply would not have looked as good at a higher aperture. The background here was a heavy blanket, but you cannot tell can you?
This photo ( https://pbase.com/bob_n/image/104517708) was taken with my very best lens and as you can see, it produces wonderfully dreamy backgrounds. This is why the pros will pay big bucks for the fast lenses.
One final note, shooting wide open allows for much more light into the camera allowing you to shoot in very dark places. Yet another reason why you pay more for the bigger, heavier and faster lenses.