Somewhere at the start of the adventure that is photography, a newer photographer will soon realize that having your subject stand out from the background, really gives the photo a near-3-dimensional effect. Your subject just pops out with the background blurred. The question of how to get blurred backgrounds in photos, is easily answered.
There are two ways to blur the background in a photography - In-camera (i.e., optical) vs Photoshop. Doing it in Photoshop is in my opinion, a boring way to spend an afternoon when you could be out Read more inside...
A valid question on how much the change in aperture affects depth-of-field, is whether an 70-200mm f/4 zoom would give you the same kind of look that an f/2.8 zoom would.
For me, a fast f/2.8 aperture is essential on a zoom lens, especially the telephoto zooms. For the same scenario, it gives me a higher shutter speed than the f/4 zoom. Or I can use a lower ISO. More importantly, since I often bounce flash in large areas, the f/2.8 aperture gives me more chance of successfully bouncing my flash than an f/4 aperture would.