The Skill Trees have three types of upgradable Skills: Player, Chest, Idle. These Skills can be bought with Skill Points, a special currency that can only be bought with Picks.
After a player has prestiged, they have the option to "transcend" a skill tree. This will allow most skills (an exception being the Infinity Scroll in the Player tree) to be upgraded an additional level. This will NOT reset the skill tree progression in any way.
**Edit (Feel free to format this better than I can)
*** The percentage increase of skill points seems to follow no set rules.
Carefully choose what skills you upgrade...
You may regret it later when you put all your skill points in chest!