Deliberately overlook something, especially something of an illicit nature. For example, They're not really entitled to a discount but the sales manager decided to look the other way. This expression uses the other way in the sense of “away from what is normal or expected.”
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.