This phrase implies a conscious decision to ignore something rather than simply not noticing it. Even with the clear evidence, he shut his eyes to the corruption.
Pro Tip 2/3
Avoidance
Used to describe avoiding dealing with a problem or unpleasant situation. Many people shut their eyes to environmental issues because they feel helpless.
Pro Tip 3/3
Negative Connotation
Often implies a negative judgment of the person choosing not to acknowledge the issue. The manager shut his eyes to the safety concerns, and now we're facing lawsuits.