When your camera is set to Aperture-Priority mode, everything is still determined for you by the camera except for the aperture. (Thus, the name.) Setting your aperture determines how big an opening in the lens lets in light. Big opening = small f-stop = small (narrow) depth-of-field. It's easier to look at this comparison of two photos shot a few seconds apart in Aperture-Priority mode with the f-stop at its smallest (left) and at its largest (right):
left: Aperture set to f1.8 (automatic setting of ISO 100 and shutter speed 1/1024 second)
right: Aperture set to f20 (automatic setting of ISO 800 and shutter speed 1/64 second)
The effect of blurring the background, referred to as bokeh, is commonly used in portrait photography to eliminate distracting details, keeping the person being photographed as the focus of the image.
Even a small change in aperture can have a significant impact:
left: Aperture set to f5 (automatic setting of ISO 3200 and shutter speed 1/32 second)
right: Aperture set of f1.8 (automatic setting of ISO 1250 and shutter speed 1/64 second)
Notice the blurring of the pot and window frame at the lower f-stop.
One thing to keep in mind as you reduce your f-stop/depth-of-field. If you are using automatic focus, it may be difficult to get the items in focus that you wish:
Both photos used f1.8, but the auto-focus chose different items to focus upon.
You can learn to control this but, for now, start by being aware of it.
Aperture-Priority mode is a good first step away from simply depending upon whatever logic is programmed into your camera---a first step in taking more control over your photographs.