Usually describes someone or something's position in a literal, physical sense on the ground or surface. The cards were laid face down on the table.
Pro Tip 2/3
Emotional Suggestiveness
Can imply vulnerability, defeat, or relaxation depending on the context it's used in. After hearing the news, she laid face down, feeling utterly defeated.
Pro Tip 3/3
Hide or Conceal
Used when something should not be seen, to keep it hidden or to create suspense. Place the envelope face down; we'll reveal the winner later.