: to see or notice (someone or something)

http://www.merriam-webster.com/dictionary/espy
Young Goodman Brown by Jack Lynch
“At least, there were high dames well known to her, and wives of honored husbands, and widows, a great multitude, and ancient maidens, all of excellent repute, and fair young girls, who trembled lest their mothers should espy them.”

When young Goodman Brown lost his faith after seeing his Faith there, he continued after the light and the noise. He saw people who he would normally see at the council board. In this passage, it is trying to say that these young girls will tremble if their mothers notice them in this kind of gathering.