A lot of this just looks like typical instagram tilt/focus filters or w/e they are where like a perfect circle is in focus but everything else is blurry. As Iacas said DoF is purely the effect of the size of the aperture used during the exposure.
As an example, here are 2 shots I took with my 55mm F1.4 prime lens. F 1.4 is an extremely large aperture and I think 1.2 is generally the largest you can get commercially, but at this aperture, the Depth of Field is so small at close ranges I can describe it as the size of a nickel or quarter. If it's not on the EXACT focal plane, it won't show up in focus. IN both of these, only the very center of the images is in focus and you can barely read that it says "Arcane" below one and "Joker" above the other.
This is the opposite of say this one which I took at F4.0
Or this which I took taken at F7.1
Lastly, this was a sunrise taken over a lake with fog coming off of it, shot at F14.0
(apologies if this shows up really big, not sure if it will automatically resize)
(For a larger panoramic click HERE)
But essentially the "larger" the F number, the smaller the aperture (less light is entering the lens) and the more "appears" to be in focus both in front of or behind the primary focal point/plane. Smaller F numbers are great for portraits because you can keep the subject in focus (face) and the background can be purposely blurred by shooting at say F2.0 or smaller.