The basic idea:
Open aperture: The wider your aperture (lower f-stop), the more light you let in. Also, the depth of field increases. That's what gives some photos that blurred effect in the background or forefront (called bokeh). Using this technique is good for a portrait, especially if you don't want the stuff in the background to really show clearly.
Closed aperture: A smaller aperture (higher f-stop), lets less light in but leaves more of the picture crisp. Better for landscape or group shots.
Buddy & Daddy are in focus. The back of the house and even the grass is blurred. I like this because I want the focus to be on Daddy's arms reaching out to Buddy.