Blurring a background can be useful to make it less distracting and separate the subject in a more effective way.
Just masking the subject and blurring the background does not work as the subject blurs into the background creating a halo around it. This can be removed by cloning some of the background over the halo, or by using the Spot Healing Brush to replace the subject with background.
Simulating the depth of field given by a camera is possible by applying a graduated blur. The Tilt-Shift Filter can be used to apply a blur gradient where the blur is less at the bottom, where the background is closer and more at the top, where the background is further away.
Applying the blur filter as a Smart Object will allow you to go back and edit the blur after applying it, as otherwise blurring is destructive and can not be undone or changed.
Add at least 20% grain to the blur, as otherwise it will not match the texture of the image. (Ref 10:00).
Backgrounds should not be sharper than the subject.
Using Box Blur rather than the usual Gaussian Blur produces a more realistic blur. (Ref, Ref)