Intelligence

Intelligence Training

Intelligence determines how much experience you can get from any source. This also gives you access to the Hacker perk, which is useful for hacking locked terminals which open leads to more valuable loot or alternate routes. Other perks under this attribute gives you access to more advanced and high-tech crafting options as well as additional interaction options to machines or robots.

V.A.N.S

The Vault-Tec Assisted Navigational System shows a trail you can follow to reach the nearest quest target. To use this, you have to press and hold the VATS button and you'll see a ghost trail leading to the quest targets. This is not necessarily a good perk to use your skill point on so just ignore this perk and use your valuable points on other much useful perks.

Medic

This perk not only improves the beneficial effects of stimpaks and RadAways, getting this perk also allows you to create a first aid centers, clinics, or surgery centers in any of your settlements.

Gun Nut

This perk allows you to modify your weapons and build more defensive traps and turrets. You'll get access to more weapon modification options which is quite useful if you want to further improve any powerful and unique weapons you come across with.

Hacker

Terminals in the game will allow you to remotely activate robots, disengage security doors or locks, deactivate/reactivate auto-turrets, and many more. This perk helps you hack any locked terminal you come across and gain access to higher difficulty terminals which you can't even interact by any other means.

Scrapper

This perk allows you to salvage rare components by scrapping unwanted junk, weapon, or armor. Take note that the component you can get will still depend whether the scrapped item is in its base form or has mods attached to it. The more modified the item is, the better components you can get from it.

Science

This perk doesn't have immediate benefits to your stats or character since it's more of unlocking additional high-tech crafting options.

Chemist

This perk extends the duration of the chems and also necessary to unlock more recipes in Chem Stations.

Robotics Expert

This perk allows you take control of robots, deactivate/reactivate them, or even initiate a self-destruct.

Nuclear Physicist

This perk helps extend the duration of Fusion Cores and improve the damage of radiation weapons. The Gamma Gun, Lorenzo's Artifact, Zeta Gun, Nuka Grenade, or any weapons with "Irradiated" in their names belong to this category.

Nerd Rage

This perk triggers when you're below 20% of your HP. Time slows down while you get damage resistance and damage boost while the effect lasts. Since the primary trigger of this perk is when your HP is reduced to 20%, it's possible to trigger it again by healing yourself above the 20% threshold, then getting damaged enough back to 20%.

Images courtesy of Fallout Wikia.