It's hard to say for sure. In cartoons, characters often have human-like emotions and could think of you out of kindness or friendship. With animals, it depends on the type and your relationship with them. Maybe a pet dog that loves you is more likely to be thinking of you.
Well, meaningful cartoon drawings usually have a clear purpose. Maybe they make us think, feel empathy, or teach us something valuable. They might use symbols, colors, or characters in a way that has a deep impact on the viewer.