Traits modify aspects of gameplay, granting a benefit in one area at the cost of hampering another. With the exception of Wild Wasteland, which has a less direct effect on gameplay, each trait modifies (and hampers) the Courier's statistics in some way; this can include Primary statistics, Derived statistics, or SPECIAL points and skills. During character creation the Courier may choose a maximum of two (with a minimum of none at all). The add-onOld World Blues makes it possible for them to re-pick the Courier's assigned traits.
Though Fast Shot and Trigger Discipline will at first appear to cancel each other out, the way the system calculates the statistics (as a multiplier effect with the base compounded as it is affected) means that both accuracy and fire speed decrease by 4% should both be selected (0.8*1.2=.96).
The Four Eyes trait is somewhat misleading in its description. The benefit it conveys is a status effect, similar to the bonus that would be granted by wearing a hat. The drawback, however, is directly subtracted from your base Perception, meaning a character with a Perception of 2 would have that value permanently reduced to 1 upon taking the trait. This can prevent the player from taking perks such as Sniper or Better Criticals, since Perks only take base stats into account when checking if the player meets the requirements. Having a Perception of one will not allow you to pick this trait.
Picking the Wild Wasteland trait allows you to obtain the alien blaster, but it comes at the cost of being unable to obtain the unique Gauss rifleYCS/186. The alien blaster is more powerful, but has limited ammunition, making the YCS/186 a better long-term weapon. This and the difference between finding the Holy Frag Grenades versus two mini nukes in Camp Searchlight are some of the most significant differences from taking the trait. Others are encountering Stripe in the Old World Blues add-on, or the availability of looting some corpses.
If the player selects the Skilled trait at the beginning of the game and decides to rebuild the character before venturing further into the Mojave Wasteland, selecting the Skilled trait again will cause its effect to stack. This leads to a gain of +10 points for every skill. This can be repeated again using the Auto-Doc in The Sink for a total gain of +15. The experience penalty does NOT stack. (Confirmed on all platforms)
Behind the scenes
As found within the game files, a medical history paper was to be filled in by the player from a texture of the actual paper; rather than a conventional menu. The paper alludes to more choices of traits than available within the final game. The history paper does not mention the Wild Wasteland trait.