What does Genesis 19:11 mean?

Finally, these strangers from out of town, these two travelers, reveal their true nature as angels by using the power of God to control a crowd of men intent on breaking down Lot's door to get at them. Neither Lot nor those in the crowd could have known that the angels had come to investigate the sins of the city in preparation for God's judgment against it.

The angels allowed the men to fully demonstrate their wickedness right up to the moment in which they would have hurt Lot and his family. Lot knew that travelers would not be safe out in the open in Sodom, and attempted to keep the men safely in his own home overnight. Unfortunately, the men of Sodom arrived and demanded the strangers be handed over for rape. Lot's attempts to discourage them failed, resulting in even more aggression.

In the prior chapter, God used human language to speak of "investigating" the sins of Sodom and Gomorrah. He also humored Abraham's attempt to plead for the righteous who might be living in Sodom. At this moment, all of these threads come together. The purpose of the "investigation" is not for God's benefit, but for ours. Seeing the reaction of the men of Sodom, the angels have provided all the evidence necessary to show that God's impending judgment is warranted.

The angels first pulled Lot back inside the door to keep him from the mob. Here, they supernaturally blind all of the men who are about to break that door down. Perhaps they did so with a blast of powerful light. Suddenly without sight, the men outside could no longer find the door. Interestingly, the text says the men were still so intent on their sin that they "wore themselves out groping for the door." This crowd is so energized by rage and perversion that even when blinded, they will not stop.

Regardless, the danger from the mob to those inside the house has been averted for the moment. A greater danger is coming, however, and the angels will quickly address this with Lot and his family.