We don't know, not for sure, what our companion animals are thinking. And we certainly have even less of a chance of knowing what's going on in the minds of wild animals.
But that doesn't stop us from trying to find out. Part of the fun of creating captions for animal images online is trying to get inside of animals' heads.
The introspective animals are, to me, one of the more interesting of the animal macros, because the creators have done more than just come up with a funny caption, as is the case with so many lol animals. Instead, there's an attempt to get at a relatively deep thought which could very well be bothering the animal in question. Sometimes, as in the case of the introspective bear, the bear is really just a stand in for a person who doesn't know what he wants (and refers, by the way, to the well known fancy cats meme), but in the case of introspective pug, I think he really is wondering whether, in fact, he is a good boy.
Of course, we'll never really know, and neither will introspective pug.