The photography method of isolating a person from the background where the background is blurry is called "shallow depth of field" (also called shallow DoF or DOF).
The way to achieve this in-camera is by using a wide aperture, the wider the aperture (the smaller the f-stop number) the less of your subject that is in focus and the more the background is blurred. You will achieve more blur if the background is further back from the subject, and you will achieve more blur with longer lenses, e.g. the amount of blur in the background when you shoot at 200 mm at f/2.8 is greater than when you shoot at 35 mm at f/2.8.
Most new photographers don't have good lenses that allow for shallow DoF. Most buy a camera (often with a "kit" lens) that doesn't have "fast glass" and doesn't open up to a wide aperture. If the widest aperture offered is at the wide focal length, and as you zoom to a longer focal length the maximum aperture is a smaller opening (bigger f-stop number) then the lens you have won't really allow you to achieve this in-camera, and you need a better lens (and possibly a better camera if you are using a camera that doesn't take interchangeable lenses).