Delicacies increase obtained dog upbringing base experience. They can be bought in the shop or found during a walk. There are the following delicacies: sausage,
cheese,
Cookie,
bone.
More detailed information on delicacies can be found here
Bonuses from the delicacies found during a walk are being summarized and added to the bonuses from the bought delicacies. If the delicacy, which was found during a walk, has a higher bonus level than yours, then your delicacy bonus will be increased.