Self definition. Many children when they first develop a strong sense of their own identity will identify things they like as "mine" with emphasis. This can go on for some months but eventually will disappear and they better distinguish what is truly theirs from other things in their environment.
It's a phaze. In infancy we cary them everywhere & tend to their needs much like a prince. This little potentate enters the toddler years expecting their parents to continue to serve their needs immediately & not interfere with their activities. As speech develops this view of the world is expressed by calling everything "mine".To include house, car, new brother, toy etc. This stage will pass as the kid matures.