Chazman, Wile E is correct, plus a little more. First of all this X times stuff is all marketing crap, means very little unless in context. There are two ways of using the X crap:
1)As Wile E said as a multiplication factor of the widest the zoom is capable of to get to the longest a zoom is capable of. As can be seen in Wile E example they are both 10X zooms, but if you wish to look at items far away, only one is useful. You can see the zoom factor means nothing, you cant tell anything from it in this example.
2)In film cameras a 50mm lens was considered normal view, so sometimes a 500mm lens was described as 10 X. This is not often used these days.
As can be seen above, these numbers mean little, just get the real number in mm, eg 300mm, 600mm.
I can see you are interested in long lenses, just for your reference they are expensive and the average person finds it hard to afford over 400mm in a quality lens. A Nikon 80-400 retails at about $3k, a second hand manual 500mm lens is about $2.5K, a new auto focus 500mm is about $11k, new af 600mm is $14k. These are quality Nikon lenses and often you get what you pay for. The 500-1200mm zooms on ebay for $300 may not deliver the same quality as the above lenses
