If you are photographing a sunset with objects in silhouette the difference will not be that obvious. If you are at a rodeo and you photograph a cowboy on the ground roping a calf a wide aperture will make the cowboy and calf 'pop'. This is desirable since such things as the audience and fences are distractions so putting them out of focus lets us concentrate on the subject instead of our eye wandering around the photo.
On the other hand if you want to photograph a street end to end, you want all of the elements to be clear so you will choose a small aperture, say f16 or less and your street will be in focus from near to far.
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