It's basically a skill tree correlated to your SPECIAL stats and each stat has it's own associated perks. You get one point per level (perhaps more as the game goes on/other conditions are met; I'm not too far into it the game).
As you descend down the tree the perks require a higher base SPECIAL stat and sometimes other prerequisites -- a certain level reached, etc. -- and most of the perks have multiple levels to them that have increased requirements as you go. You can also spend points on leveling up the SPECIAL stats themselves. It's actually not really different from prior games in the end result, it's just implemented in a bit less of an old school RPG fashion.
The lockpick perk, for instance bumps you up a level of lock difficulty for each level of the perk you have.
I can see some people being upset they can't dump all their perks into one thing -- say lockpick, hacking, or charming -- early on like you could in 3/NV, but I like the system well enough.
Training manuals, instead of giving you a point or two in a perk, give you specific bonuses per manual found. Wasteland Survival Guides, for instance, will raise your damage resistance or some such.
Overall I like it but like I said, I can see how it may have detractors.