Your description shows two matters—the equivalent focal length range and the "optical zoom" ratio—but really, it's easier to understand by dividing them to three different ones:
- Minimum focal length (in millimeters, easiest to compare with the 35mm equivalent)
- Maximum focal length (same note)
- Zoom ratio
If you know two out of the three, you can easily calculate the third, either by multiplying or by dividing.
Notice that I use the word "ratio" to describe the "optical zoom" you mentioned, as it is simply the ratio between the maximum and the minimum focal length of a lens. In the example you've given, it is
250mm / 25mm = 10. There is no unit of measurement for the ratio, because of it being a ratio; the 'x' often appended to it is for "times," and it basically means "the maximum focal length of the lens is 10 times longer than its minimum."
The zoom ratio can be very useful and easy to understand when comparing compact/point-and-shoot cameras, because most of them have a very similar, or even identical, minimum focal length, so the same ratio means basically the same thing across different cameras/lenses. But it becomes pretty much useless with lenses for interchangeable-lens cameras, or with more specialized cases of fixed-lens cameras.
Let's take, for example, two popular types of lenses that many photographers use with interchangeable-lens cameras: a 24-70mm and a 70-200mm, or their rough equivalents. The zoom ratio for both is approximately 3 (70 / 24 = 2.92; 200 / 70 = 2.86), so if you didn't know the focal lengths themselves, you could have understandably mistaken them to be identical lenses. But in reality, they are radically different: the first starts at a wide-angle setting, and zooms into a somewhat tighter angle of view, while the second picks up exactly where the first ended (notice the same 70mm mark) and zooms in tighter from there.
Another example worth mentioning is the Sigma 50-500mm lens. You can see that its zoom ratio is 10, exactly like the example you gave, but its minimum focal length is longer—instead of a wide-angle view, you get what's called a normal field of view—and it gets tighter at the end of the zoom range.
The equivalent focal lengths are a lot more useful than the zoom ratio, because they can tell you exactly the kind of field of view you should expect. Try to grasp the concept, and understand it through some experience, too. Also try some focal length simulators online; the best one I found is
Nikon's .
