Pathfinder Society Organized Play allows players to advance either 1XP or 1/2XP per session. There are no advantages offered by taking the slower XP (experience) gain, so why would someone use this option?
The relevant bit of the Pathfinder Society Field Guide:
Primarily, the "slow" XP gain is so that you can keep playing with a particular character longer. Note that when you gain a level you pick whether you are on the slow or normal track for the next level. There are a couple of reasons you might do this:
Hypothetical 1: I like playing PFS with my friends, but I attend more games than they do
I might decide to do ½ XP for a few levels, so that I'll stay in the same tier with them.
Hypothetical 2: I really love this character, but I'm approaching the level 12 cap too rapidly!
I might then do ½ XP to prolong the life of that character.
Hypothetical 3: I GM a lot of PFS games, and all of my characters are getting XP, but I've not had time to play them
Might choose ½ XP for a level or so, in order to actually get to play the character at that level.
In the end, it's just a way to stretch out the pacing of PFS games, since there's not a lot of end-game content at level 12, and if you play a lot, you'll be leveling up fairly quickly.
I've found with newer players that the longer they play a level the better grasp they have on the class and character, as they can spend more time mastering and getting comfortable with the abilities/feats/spells.
The reason I chose to do this when I played is so I can understand the classes better that I never play at a non-organized play setting. This allows me to find the classes quirks and as a DM helped me challenge my players that played the classes I never played before. It also helped me realize that I really enjoy the Witch class.