Skill Tree Examined. The Skill Tree can be used to link skills gained between all the different team members of your party. There are 5 skills each team member can share from another team member. So, if there are 6 team members in your party, this would mean you have an additional 25 skills you can use. Some skills cannot be shared.
Skill linking is dependent on the affinity level between characters as well as how many affinity coins you have received. Affinity coins are gained from defeating bosses and unique enemies. The more useful abilities cost more affinity coins. In the image, the player cannot select the skill they want because it reruires 7 coins and they only have 6 left of 64. They need to unequip a skill which will free up the coins.
The shapes represent what kind of skill can be linked, different shapes mean different kinds of skills. When a shape has a yellow border, you have the required affinity level so the shape is unlocked. In the image, Shulk has maxed out affinty with Reyn and Sharla, but has very little with Riki or Melia.