"Righteousness" has an internal meaning that is very similar to that of "meek"; it has to do with the love of doing good things for other people. In the prior verse, then, the Lord addressed those who were already in that state; here He addresses those who "hunger and thirst" for that state.

Hunger represents the desire to want what's good, despite the craving for what is evil (sort of, "I'd like to be craving celery right now, despite the fact that I'm actually craving chocolate ice cream"). Thirst represents a lack of knowledge about what is good, and a desire to learn.

This verse, then, says that those who want to resist evil and delight in being good instead, and who want to learn what they need to know to make that change, will get what they're seeking.