By having a softer background, the subject will be separated from the background and pop a little bit more. Also, our eyes will focus more on the subject and less on anything distracting in the background.
Shooting wide open at f/2.8, f/4, or f/5.6 will give us the minimum amount of depth-of-field. So I almost always shoot wide open (f/4 on my 600 mm lens) to help blur the background and to increase the shutter speed. Since more light is getting through the aperture, the shutter doesn’t have to be open as long.
Use a longer lens the more telephoto power you use, the less depth of field you'll have so the background will be more blurred. Long telephoto lenses have a very narrow depth-of-field, this will help separate the subject from the background. A 600 mm lens gives a softer background than a 400 mm lens.
Use an extender to increase the effective focal length. By using a 1.4 Extender and making a 400 mm lens effectively a 640 mm lens, there will be less depth-of-field, and the background will be more blurred.
Use an Extension Tube to help blur the background. An Extension Tube (usually used in macro-photography) allows your lens to focus closer; this diminishes the depth-of-field so that the background will be blurrier.
Get lower or move to the right or left to improve what's in the background sometimes by moving lower you can get the sky in the background and not a cluttered bunch of branches. By moving right or left, the background will change as well, so move a little each way to see if the background can be improved.
Have distance between the subject and the background the further away the bird is from the background, the more it can be blurred. Sometimes you have control of this and other times you don’t but if you can shoot where the background bushes or trees are further away, the better the image will look.
Use a full frame sensor; a full frame sensor has less depth of field than a cropped sensor. A cropped sensor like the Canon APS-C on the 7D Mark II has more depth-of-field than a full sized frame on a camera like the 5D Mark IV.
I hope this helps, if you have other ways to blur the background, please leave them in the comments section below.
Thanks as always, Tim