[Most Happy] are the meek, for they shall inherit the Earth.
This is of course a reference to the Old Testament:
But the meek will inherit the earth; and shall delight themselves in the abundance of peace.
This Psalm is speaking of the present day, the present Earth. Evil doers will be cut down. You shall be fed. Commit your way to the LORD and He will bring it to pass. These are all current realities, speaking of this life.
All throughout the Psalm, the writer is speaking of trusting in the Lord, and the Lord acting on behalf of the faithful, both in this life, and, in light of the New Testament, also with the promise of the next.
An Example of Meekness
Using scripture to interpret itself, then, we can look for godly examples of meekness in the Old Testament and notice the result.
A good example is Hannah. She was child barren, and more than that, the other wife of her husband was mocking her for it. Instead of lashing out and retaliating, she went to prayer in the temple. She was a picture of meekness. Crying out to God without uttering a word, she asked God for reprieve. After being misunderstood by Eli and being falsely accused of drunkenness, God promised her a son through the prophet. Samuel was born to her in response to a prayer which didn't utter any words. Thus, she received a son whose words never fell to the ground.
Meekness as a way to Receive
Thus, we can see that God's answer to Hannah was to give her the things of this life--a son. So, it appears that "inheriting the Earth" is receiving the things that others fight and contend for by not forcing to get your own way. God's way of receiving the things that the world pushes for is by not pushing, but by meekness.
This is consistent with the Psalm, because the whole intent of it is to rely on God.
Another example would be David. Although he at one point took a piece from Saul's robe, he purposed in his heart not to take the kingship which he was promised by force. Instead, he waited his time, hiding in a cave when necessary, and the kingship was delivered to him at the appropriate time. In retrospect, the later cursing by Shimei while David was fleeing from Absolom is important, then, because it was the exact accusation that Shimei was pointing at him. Because he hadn't taking the kingship by blood, but allowed it to come to him in God's time and way, Shimei's cursing was unjust, and David was not guilty of his words.
The point of the beatitude as a whole, then, is that we can be "Most Happy" when we are not forcing to get our own way, because we know, in due time, we will inherit the very thing that everyone else is fighting to own. In this knowledge, we prefer the path of meekness, with the knowledge that,
A little that a righteous man hath is better than the riches of many wicked.
While the Old Testament passage did not have the knowledge of Eternity, however, we see that the concept is extended, to both in this life and in the age to come (Mark 10:30). Christ, being the perfect example of meekness as the lamb upon the cross, receives the fullness of this inheritance through His crucifixion.