What does so, one night the farmer crept out of the house as quietly as a mouse. mean?

A simile is used in this sentence. A simile is a type of figurative language and it's when you use "as" or "like" to compare things that have nothing to do with each other. So, here it's used to show that the farmer crept out extremely quietly. Since mice are very quiet, a simile is used to make a comparison between the farmer's quietness and mice.