I'm new to photographing. But I'd like to know what 10x zoom means in meters. I know that it means the picture is enlarged 10 times, but what does it mean in meters?
I mean does it mean like the picture I see from 10 meters away, is like 1 meter away when I use 10x zoom? Or does it mean 10 feet away is like 1 feet away with 10x zoom?
It's impossible to say.
This is because a "zoom factor" is a relative measurement, not an absolute one. 10x zoom doesn't mean the picture is enlarged 10x. All that the zoom factor is telling you is how much longer the longest focal length of the lens is from the shortest one.
Both a 5-50mm and a 50-500mm lens are 10x zooms. But they have vastly different types of reach. And on different sensor sizes, that amount of reach also changes, due to crop factor.
See also: How do zoom, magnification, and focal length relate?
A 10x simply means that the longest (most "zoomed in") focal length is 10x longer than than widest focal length. This has the effect that everything in the photo is 10x bigger. It's a ratio, and doesn't have any meaning in meters or feet.
It doesn't mean that it's as if you were 1 foot away instead of 10 feet. In fact, if you took photo with a wide angle lens, say 20mm, from 10 meters and crop it sufficiently, it will have the same composition as a picture taken with a 200mm lens at 10 meters (the quality will be much worse, but the spatial relationships between objects in the picture won't change; they will, however, change significantly if you move to 1 meter).
I suggest you try moving toward and away your subject with different focal length, you get very different compositions; a "zoomed in" picture tends to compress depth, whereas a wide lens will accentuate depth
As @inkista explains, the "times-zoom" notation is just a relative measure, and doesn't tell you anything absolute. This is different from binoculars, where the number actually means how much bigger the subject appears than with the naked eye — that's because cameras project what's known as a "real image" onto the sensor or film, whereas binoculars form a "virtual image". (That's a tangent, but read more on that here if you're curious.)
So, anyway, the only way meters and feet make sense here is also in relative terms. If you know that at a certain distance, an object one meter across fills the whole frame when zoomed in on a 10× zoom lens (a 50-500mm lens, for example), you know that you could fit 10 meters across that same frame zoomed out.
(Do be aware, though that this will be approximate, because the numbers aren't meant for scientific measurement and are not likely to be precise.)
