see the light

Also, begin to see the light. Understand or begin to understand something; also, see the merit of another's explanation or decision. For example, Dean had been trying to explain that tax deduction for fifteen minutes when I finally saw the light, or Pat was furious she and her friends were not allowed to go hiking on their own in the mountains, but she began to see the light when a group got lost up there. This term, dating from the late 1600s, originally referred to religious conversion, the light meaning "true religion." By the early 1800s it was used more broadly for any kind of understanding. Also see light at the end of a tunnel; see the light of day.

The verb has one meaning:

Meaning #1: change for the better
  Synonyms: reform, straighten out