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A myth. They're turning their eggs in a nest dug in the ground.
Where it came from
Pliny the Elder wrote in the 1st century that ostriches hide their heads in bushes and think their whole body is hidden. The image was too good not to keep.
What’s actually true
An ostrich would suffocate with its head in sand. Ostriches lay their eggs in a shallow hole in the ground and several times a day lower their heads into it to turn the eggs. From a distance, the bird appears to have no head.
When threatened, an ostrich either runs, at up to around 70 km/h, or lies flat with its neck along the ground, or kicks. It does not hide its head.
Further reading
- Wikipedia: Common ostrich (Behaviour)