I think that it means we are the be extremely zealous in actively pursuing virtues and doing mercy (which is the next beatitude), this is the will of God, and in doing it we will receive what we are after.
The hunger relates directly to His will for the Lord Jesus says "My food is to do the will of Him who sent Me," (that we are to do the same is proven in many places) and the thirst relates to the righteousness Jesus satisfies us with for He also said "whoever drinks of this water which I will give to him will never be thirsty for eternity, but the water which I will give to him will become in him a well of water springing up to eternal life."
By this active pursuit we will obtain ("be satisfied") for the Lord also said "everyone who asks receives, and the one who seeks finds, and to the one who knocks it will be opened," in this same lesson.