To look away as if you did not see what you really saw.
Usually used to describe someone ignoring something that they really saw (possibly something wrong or illegal). Most of the time, it has a negative connotation but does not always. See the examples below.
The neighborhood children were stealing from the apple orchard. The owner turned a blind eye because he knew they were poor and hungry.
The woman saw her co-worker, Nini, take money from the petty cash drawer. She turned a blind eye because she knew Nini had not told their boss about her many times being late for work.
Many apartment dwellers wish their dog-owning neighbors would do the responsible thing and clean up their dogs’ messes. However, many just turn a blind eye to this selfishness in order to keep peace in the community.