In some menus, these are also called Unique Squad Member Powers. With that name, it's not a surprise to say your squadmates are also key to unlocking the bonus powers. The function of the Advanced Training is pretty simple - it allows Shepard to pick up a bonus power that's based directly on one of his squadmates.
One key pillar of this is the Bonus Powers that Shepard can recieve - one extra power that's picked via the Advanced Training research project that becomes available part-way through the game. The RPG systems in Mass Effect 2 are streamlined when compared to the first game in the series, but in many ways ME2 offers improvements and adjustments to make the role-playing progression you can do more satisfying.