“Zooming with your feet” means getting closer to your subject physically instead of relying on a longer lens, but you should be aware that the results you won’t be the same. Here’s a 9-minute video from This Place that looks at how different focal lengths affect perspective when compared to “zooming with your feet.”
Perspective distortion is often misunderstood — it’s an area of photography that many photographers may not need to explore or understand properly. Yes, there are problems with particular lenses, including distortion from the glass and other things, but changing the focal length wouldn’t adjust perspective in a theoretically perfect lens. Look at this animation, which has no optical distortion in the hypothetical camera’s glass:
You can see that the field of view changes only in that it’s a closer crop of the scene — there’s no warping or distortion at all.
But when you physically move your camera closer to the subject, you’re changing the perspective itself. You move through the scene, seeing new angles and behind objects. This next animation shows the effect of moving the camera through the scene — on the left you see the full field of view, and on the right you can see a cropped in version highlighting how the subject’s face changes:
Watch the full video above to get a better understanding of things like the dolly zoom and perspective distortion.