The others are correct - these are racial maximums that can only be exceeded by the Exceptional Attribute quality. You can only go higher than that limit via some form of augmentation (magical, cybernetic, bioware, etc.) and that boost is limited to 4 higher than your current maximum.
Example: Dee-Aitch the dwarf street samurai has a racial limit of 5 to his Reaction attribute. He takes the Exceptional Attribute quality for 14 karma to increase that to 6. He can increase that by four more points using augmentations, in his case, Wired Reflexes 2 and Reaction Enhancers 2, giving him a final Reaction score of 6(10). If he had not taken Exceptional Attribute, he couldn't go higher than 5(9).
Example 2: Sparkle the elven face is negotiating for her team. She's quite the looker with a great personality, and her charisma is close to the max at 7. The team's mage, Fingers, wants to ensure things go smoothly and that the team gets the most money possible for the job, so he casts Increase Attribute (Charisma) at force 7 on Sparkle. He rolls well, getting 5 hits, which would be enough to increase her Charisma to 12. However, one hit is wasted, as Sparkles' maximum augmented Charisma is limited to four higher than her Charisma score, leaving her with Charisma 7(11) for the negotiating session.