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When a camera says that it has, for example, a 10x optical zoom, what exactly is that 10x based on? Is it the angle of view of the human eye, the focal length of the camera, or what?

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It is simply the ratio between the longest focal-length and the shortest focal-length of the camera. For example, if the camera has a 25-100mm range, its zoom is 4X because 100 / 25 = 4.

It does not matter if this is computed based on the actual or equivalent range because the answer will be the same. More importantly, is that two cameras with 10X zooms can have very different ranges, say 25-250mm and 35-350mm, which is why it is better to look at the actual equivalent focal-length instead of zoom ratio. Between these two examples, one camera is much better of architecture (starting very wide at 25mm) and the other for wildlife (reaching much longer at 350mm).

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    \$\begingroup\$ "More importantly, is that two cameras with 10X zooms can have very different ranges" - a very valid point I overlooked. +1 for that! \$\endgroup\$
    – Chait
    Commented Jan 7, 2013 at 20:22
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Simply put, it is the ratio of maximum focal length to minimum focal length.

In your example, your optical zoom would be specified as 10x, if your camera has the minimum focal length (when you zoom out completely) as let's say 16mm, and the maximum focal length (when you zoom in completely) as 160mm - then the X number would be 160/16 = 10X.

Look at The Truth About The “X” Optical Zoom if you want to learn more about how that works.

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