Cats have many moods and behaviours. Reading a cat's behaviour can mean the difference between enjoying the cat and being injured by one. Cats are instinctively cautious creatures that tend to not trust anyone or anything until said person or thing has earned it. Watching for signs of submission in a cat will let you know if you've achieved that trust.
Crouching down is one way cats show submission. When a more dominant cat or its owner approaches, a submissive cat will crouch down. This lets the other cat/owner know it is not a threat.
Lowering the Tail
In addition to crouching down, a submissive cat might lower its tail as a sign of non-aggression. The tail will be lower than the line of its back, and it'll be crouched down. Sometimes, the tail might even be tucked around his feet. Both are submissive behaviours.
Flattening the Ears
Although it might look like a sign of aggression, a cat will flatten its ears when it is being submissive. The cat might be in a submissive fear, but it is still a submissive behaviour.
Laying on Side With Upper Paw Raised
When a cat lies in this position, possibly with its owner or a more dominant cat, it is saying it submits, with one exception. The upper paw is this way because though the cat is relaxed and submissive, it is ready to strike should the need arise. When a cat is in this position, it is not long before it decides he's had enough and strikes--sometimes without warning--and runs away.