If taken at levels 3, 6 and 9, the amount of experience received from it allows to gain "extra" level once the player would normally reach level 17 (17700 XP compared to 17000 XP difference between levels 17 and 18).
With a level cap of 20, Swift Learner is worth 2,090 XP at level 2. With a level cap of 30, it is worth 6,570 XP at level 2.
There is much more experience in the game than is necessary to level to either 20 or 30. This perk increases the rate at which the player character will reach max level. Once max level is reached, the perk ceases use.
This perk stacks multiplicatively with the XP gain boost from difficulty level in Fallout 3, as well as the XP gain boost from Well Rested. For instance, on normal difficulty, Swift Learner provides 10% bonus to the base XP earned; on very hard, Swift Learner provides 15%; on very easy, Swift Learner provides only 5% to gained XP (Fallout: New Vegas removed the experience differentials between difficulties).
In Fallout: New Vegas, this perk is less useful compared to the Lonesome Road perk Lessons Learned. Giving an extra +1% for every level earned (+26% at level 26, +27% at level 27) rather than 10%, but it has a level 26 requirement while Swift learner requires level 2.