The training tab includes Skills and Traits. They can be hard to tell apart, but have different shapes. You unlock them one at a time by spending hero points. They are unlocked in order along multiple tracks that can be completed in any order. You can start training Elite skills and traits once you have completed all the core tracks.
Skills are mostly active and equipped in the skill bar of the UI. Traits are always passive and equipped in your hero panel. There used to be minimum level to equip traits, I’m not sure if that was patched out.
All traits belong to a specific trait line. To equip a trait, first you must choose the trait line. This will equip 3 minor traits (if they are unlocked), and then allow you to choose 3 of 9 possible major traits.
You can choose up to 3 trait lines, so in the end you will have 9 minor traits and 9 (of 27) major traits. An Elite spec is nothing more than one of two slightly overpowered trait lines, with a minor trait that unlocks a new weapon and other abilities. You cannot select both Elite trait lines at the same time.
The passives often interact and can significantly affect game play, so have fun experimenting with them!