Points
From MHWiki
Each mouse caught is worth a specific number of points. These points are a tally of the experience of the hunter. The number of points a hunter has places him into a certain category, such as Novice, Apprentice, Journeyman, Master, Grandmaster, Legendary or Hero. The points allow the hunter to travel to different areas.
Points are gained by catching mice. The heavier the mouse is, the less points it is worth. Since a smaller mouse is faster, it is more challenging to catch, and therefore worth more points.