Most of the commentaries I consulted about this verse agreed that the Lord specifically meant mourning over sin. I tend to favor this interpretation because it fits the context of the sermon, flowing well from Matthew 5:3 and the idea of facing our own spiritual and moral bankruptcy.Blessed are those who mourn, for they shall be comforted. ~~Matthew 5:4 (ESV)
First and foremost, I need to ask myself whether or not I grieve over sin in my life. If not, I clearly need the Holy Spirit to readjust my perspective until I understand how He feels about it. Each time I go against His moral standards, even in ways that seem insignificant, I forget that Jesus bled and died to atone for that thought, attitude or behavior. My sins offend a holy God. He paid a terrible price to save me from their eternal consequences.
The first time I mourned over my sin, God allowed me to go through two gut-wrenching weeks of despair, knowing that I had failed to meet His righteous standards. But when a friend helped me understand that Jesus paid for my sin on the cross, accepting the punishment as though it belonged to Him, the Lord gave me the comfort of His forgiveness. And He gives me that comfort as I mourn over my present sin.
Secondarily, believers should mourn over the sins of others. I think of this point in juxtaposition to the unbridled glee that many people have exhibited this week over the exposure of Josh Duggar's molestation of his sisters. Those who rejoice in how this public revelation holds Duggar and his family up for ridicule display a horrible lack of love, since love doesn't rejoice in wrongdoing (see 1 Corinthians 13:6).
Certainly, Duggar committed a terrible crime, and sinned against a holy God. I can't justify his actions. But many people, rather than grieving that this young man violated his sisters, lost his own innocence, betrayed his parents' trust and sinned against God, unabashedly celebrate this "evidence" of Christian hypocrisy. What an inappropriate, self-righteous attitude!
Sin, whether our own or that of someone else, should create deep sorrow in us. Jesus assures us that He will comfort us in such mourning, and I trust Him to be faithful.