The notion is that the supposedly dumb ostrich believes that if it can’t see its attacker, then the attacker can’t see it.
Today, "don't bury your head in the sand like an ostrich" has come to mean refusing to think about unpleasant facts, even though they will have an influence on your situation. But, actually, ostriches don't, and never did, bury their heads.
Thanks to their keen eyesight, ostriches (the world's biggest bird) often spot a predator, such as a cheetah or lion, before it sees them. In response, the birds may flatten themselves to the ground to appear like a large (if feathered) rock or mound. They don’t stick their heads into the ground, though.
If they are spotted, flightless ostriches have a much better way of escaping danger: running very fast in the opposite direction. These birds make up for their lack of airborne ability with super speed - they are the world’s fastest two-legged animal, capable of reaching speeds of up to 43 mph (70 kph). That's slightly slower than a lion, but the ostrich has much greater stamina. Outrunning a cheetah, is a more challenging proposition.
The head-burying myth, says Discover Wildlife, may have stemmed from the fact that the ostrich digs into sand to create a nest. As large flightless birds, ostriches cannot nest in trees, so the male scrapes out a hollow in the ground with his beak. This could look like he is burying his head in the sand.