In Johnathan Edwards work "Sinners in the Hands of an Angry God" what does this quotes mean? "Haste and escape for your lives, look not behind you, escape to the mountain, lest you be consumed."

He's saying to escape the life of sin before it's too late, that Gods wrath is coming.

God's wrath is coming, do your utmost to escape before it's too late. In context, if I remember correctly he is referring to the destruction of Sodom and Gommorah. Lot's wife looks back and turns into a pillar of salt. During the days of his ministry, he might have used this as a warning to to his congregation, telling them to flee from their past lives and live a Godly life ... not looking back to the sin and lives they've escaped.