Animals tend to make people feel better and some people need a distraction more than anything else. The dog or whatever animal it is can help reduce the stress by provding them with the proper distraction. Animals are cute and cuddly and in general make you feel better and want to play and relax.
I'll assume this is in regards to household pets, rather than animals in general (I sincerely doubt trying to escape the wrath of a wild grizzly would reduce ones stress). Household pets certainly can reduce stress, but they can also be frustrating and add to it. Especially when they are young, and you're trying to teach them the rules of the house, or when they get old and decrepit, and may lose bowel control or other such downsides of old age.
However, a healthy and obedient pet most certainly can reduce stress. For instance, cats and dogs enjoy being petted, as it releases hormones (not sure what they are called) that make them happy. A similar response is triggered in the person who is doing the petting. For obvious reasons, this can reduce stress.