How to blur the background in photo booth?
Photo Booth in macOS Catalina no longer has the option for custom backgrounds. If you have an older version of macOS, you can add your own background, which you can blur.

Take a picture using Photo Booth without you in it, such that it captures the background.
Blur the image using a photo editing application, such as Photoshop or one from Tool to quickly hide/blur/redact text in screenshot?.
In Photo Booth effects, on the last page for custom backgrounds, drag your image in.