Parallax might sound like a very complex term, but it is easy to understand. It is a kind of error that comes in the position of a fixed point or object, if it is viewed by two different points in the same plane. If you still do not understand, then try this. Hold your index finger in the straight line in front of your nose. Now close your one eye and view it from the other, one by one. You will see a difference in position even though you have not moved your finger.

In a single lens camera, the viewing lens and the capturing lens are same. The frame that you see in the view finder is actually the image that is made on the capturing lens and reflected by a mirror onto the view finder. Hence in a single lens reflex camera there is no parallax.
Now talking about home cameras and twin lens cameras, such as the Sony Alpha 200 with its twin lens kit, you can see in the picture on your left that the lens from where you view the frame is different from the one that captures it.

Now see the figure above. The image formed at the view finder is a little above the image formed at the lens. This change in position causes a vertical parallax in your picture. now you would know that why is it that when you click from your home cameras or the twin lens cameras, there is more headspace in your actual picture than what you framed. This is because of the vertical parallax caused due to two different lenses.