These verses are entered to show the way in which the pride of the Limhites was destroyed. While the end of verse 10 suggests that they were becoming humble, the military sorties of verses 11 and 12 show that this humbling was not complete. Somewhere, somehow, there were still those with a pride of arms that told them that they could defeat the Lamanites that were surrounding them. The third defeat finally showed the error of that pride, and they finally begin to humble themselves.
The humility of the people took two forms. The first was the resignation to the Lamanite's conditions. They because humble as a defeated people is humble. They allowed themselves to be "smitten, and to be driven to and fro, and burdened." While this is a logical consequence of the terrible losses they would have suffered, it still isn't the type of humility they needed. That finally comes in verse 14. They humble themselves before the Lord, realizing that only He can save them. They no longer have pride in their strength of arms. They no longer believe that they are able, of themselves, to extricate themselves. In this great extremity, they finally call upon the Lord.
This recognition of our relative position before God is the type of humility He requires of all of us. We need not be beaten down to find it, however. We can enjoy his great blessings and yet acknowledge Him and His guidance. The Limhites had become so filled with pride that they had to be torn down before they could be built up again. However, what God wants is the humility, not the process by which we develop it.