Q:
mastery points
You need 2 components. 1, the xp (which you have) 2, the mastery point. These can be found on map, or for achievements. Once you have sufficient of both for the line your mastering, you have to open the mastery panel and choose to level it up. This does not happen automatically. Then choose the next item you wish to work on.
Dulfy has great guides for each of the Heart of Thorn maps to get the mastery points. Here is her guide to Verdant Brink Mastery Points and Strong Boxes
You should be gaining experience as you traverse the maps and do events (experience boosters help make it faster). Once you have done enough mastery points you should be able to go into the Mastery Tab of the Hero panel and spend the points on what you have opened up. You can choose which line to put your experience in so be careful and look at them all before choosing which completed one to spend the masteries on. I recommend gliding first and then the mushroom jumping. Those get you off to a good start.