With wild dogs/wolves, prolonged eye contact is seen as a challenge or a threat, but, with domesticated dogs, it does depend on the dog's personality as well as the person. There was a study conducted by researchers in Japan earlier in 2015 suggesting that eye contact between a dog and his/her owner can cause increased levels of oxytocin, the "hug hormone," in both parties. We can't know what exactly is going on in a dog's head, but if you and your dog have a healthy bond with one another, prolonged eye contact from your dog can be compared to them giving you a hug.

Here's an interesting article from the New York Times that goes into more detail about the research:

http://well.blogs.nytimes.com/2015/04/16/the-look-of-love-is-in-the-dogs-eyes/?_r=0 (http://well.blogs.nytimes.com/2015/04...)