Genesis 19:11-14 meaning

The angels reveal their supernatural character, they struck the men who were at the doorway of the house with blindness (v 11). Then the mob cannot do what they intended, with an inability to see properly (2 Kings 6:18, 20; Acts 9:3, 22:6, 26:13). It is amazing that this did not seem to deter the mob from pursuing the fulfillment of their lust. They wearied themselves trying to find the doorway (v 11). You would think if they lost their sight they might worry about getting their sight back as a priority. 

The angels ask Lot, "Whom else have you here?" (v 12). They tell him to gather his family and leave the city because they are about to destroy this place (v 13). The angels announce the coming destruction of the city. The city will be destroyed because their outcry has become so great before the Lord (v 13). This refers to the allegations of Genesis 18:20-21 which prompted Abraham's intervention for the righteous (Genesis 18:22-32). The Lord has sent the angels to destroy it (v 13). The outcry and allegations had been proven true beyond all doubt, consequently, the city will be judged, and punishment is inevitable.

It is worth reflecting on the power wielded by these two angels. They are formidable beings, able to inflict massive destruction.  

Lot went to warn his sons-in-law, who were to marry his daughters (v 14). Lot had allowed his daughters to become engaged to young men who lived in Sodom. Lot tells the young men "Up, get out of this place, for the Lord will destroy the city" (v 14). But he appeared to his sons-in-law to be jesting (v 14). It seems his sons-in-law considered the message ridiculous, unbelievable and too fantastic to be taken seriously. There could be many reasons for this. They might not have believed in or followed the LORD. Or they might not have believed a mere man could know such a thing. In any event, they chose to ignore their future father-in-law and trust in Sodom.