Aperture is one of those "scary" terms and one I know I shied away from for years and years....but it was Kim Thunder of Kim Thunder Photography in South Africa who finally explained it to me in a way that made sense.
For the layman (like me)....your camera lens is basically like your eye, try looking at an object with your eyes wide open - go on, do it now - do you notice that only the item you are looking directly at is in focus and everything else around it is out of focus i.e. slightly blurry? Now try squinting your eyes and looking at the same thing, suddenly both the item and everything around it are in roughly the same focus.
Imagine that when your eyes are WIDE open it is the same as your lens being WIDE open basically a WIDE aperture, this is show as a small number i.e. F1.4 and is brilliant for macro photography and portrait work....this term is also refereed to as a shallow depth of field.
"Dandelion Dreams"Using a wide aperture to create the shallow depth of field which results in the grass behind the children being in less sharp focus then the grass in front of them.
"Busy Bee"Taken with a shallow depth of field using a macro lens to ensure the grass behind the bee is out of focus and doesn't detract from the subject
When your eyes are squinting or "smaller" it is similar to small or narrow aperture, depicted as a high number F8 and allows everything to be in focus, exactly what you need when shooting scenery or landscape photography - basically a deep depth of field.

"Daffodil Row"
Taken with a deep depth of field so that both the line of flowers and the background line of trees are in focus
"Children on the Beach"Taken with deep depth of field so that both the children and the cliffs are in focus
Most modern cameras (unless it is a little point and shoot) will allow you to control your aperture while the camera works out the shutter speed for you and this can be very useful if you are trying to shoot a subject in front of a very cluttered background, this is known as the Aperture Priority and is referred to on the camera as the A mode or Av mode, check out your camera manual for more information on where to find this feature on your camera.
All the above being said, I have found the best way to get to grips with this concept is to get out there and play around with the camera - the beauty of digital is that you can and just discard the photos that don't work.