At least some of us humans use our hand quite a lot while communicating to each other. We wave our hands, point, some cultures shake hands, and some of us gesture wildly. While parrots aren't quite as lively with their limbs for communication purposes as we are, they can- and do use their wings and feet in many different ways except for getting around.
It's easy to think that the joint in the middle of the visible part of a bird wing is the elbow. In fact, this is the equivalent of our wrist! The flight feathers that are attached to the hand, which is the outer half of the wing, are called primary feathers. The flight feathers on the arm are called secondary feathers.
Flapping and extended wings
Flapping while still on a perch is often observed in young parrots that are just learning to fly, in older birds that have had their wings clipped or have otherwise been deprived of flight, when a bird looses it's balance, or as an aide when climbing up something at a steep angle. We can also see flapping or standing with the wings fully extended during conflicts between birds, during warning or threat displays, as well as during play.
Some species, especially cockatiels and some other australian cockatoos will sometimes spread their wings and tail feathers while hanging upside down, often referred to as the "bat bird." Parrots might also flap vigorously when they feel threatened, even if they can't fly away. This can result in serious injuries if we are not careful when handling parrots.
(Warning: this video might raise your insulin levels!) Baby parrots like this young blue and gold will start flapping their wings while they are still in the nest, before they have their flight feathers. At this stage they don't yet have the energy to do it for very long, though!
1.4 WINGS AND FEET
This bonded pair of adult blue and gold macaws are politely telling the onlookers to "F right off." The bird furthest to the back is extending it's wings as part of this display. It would be very unwise to put your hand close to either of these birds in this moment.
Holding the wings out from the body
We sometimes see parrots hold their folded wings out from their bodies. This is commonly observed when parrots are warm, as a part of helping them control their body temperature.
Some species, especially males, will hold their wings out from the body while the wings are still folded or slightly drooping during courtship. In this situation they might walk back and forth, often making little noises, eventually mounting or trying to mount partner. Male cockatiels and ring neck parrots will hold their wrists out from their body while the tips of their primary feathers are crossed over the tail feathers, often while whistling and singing, as part of their courtship behavior. This is often referred to as "heart wings" because it looks like they are forming a heart shape with their wings when observed from behind.
This male Eclectus is holsing his wings out from the body while still folded, although slightly drooping.
We will sometimes see parrots hold their folded or partially folded wings out from their bodies while shaking or moving them slightly up and down. This usually happens in situations where a bird is confined to space or a situation either because it is caged, deprived of flight or has poor flight skills, or otherwise can't escape from- or get closer to something, possible because a lack of alternatives perches or places to go, or something like pain that might hinder it from taking flight. Often, this behavior is accompanied by round eyes, tight feathers on most of the body and a more horizontal posture. The parrot might also scream or vocalize, and we will sometimes observe a darting gaze as well as moving from side to side or lifting the feet.
Parrots can stretch in a variety of different ways. Just like how you might stretch after sitting at your desk for a while and transitioning to a new activity, we often see parrots stretching after they have been sleeping, resting or preening, or right before they settle in to do so. You will for example sometimes see them lift their still folded wings upwards, extend and fold the wings repeatedly, or do a "figure skating pose" where they extend one leg and one wing backwards, simultaneously. Note that many of these movements can be used in other contexts than stretching as well.
Left: Galah stretching it's left wing.
Right: African grey stretching it's folded wings upwards. This type of movement is seen both as a stretch in the context of settling in, preening or waking up, but similar movements can sometimes also be part of aggressive displays, especially when we see it together with pinning eyes, fluffed back- and neck feathers and vocalizations.
Sometimes the wings might not be fully folded when a parrot is resting; it can look as if they are drooping a bit. This is sometimes seen in baby birds that have a tendency to figuratively "melt" or display a generally very loose body language before- and a while after they are fledged. It can also be observed in older birds, in which case it is often a sign of illness. This is especially true when the wrists of the wing are closer to the bird's head than normal, sort of like what our shoulders look like when we shrug, and the bird is resting a lot. If your parrot is showing these symtoms, contact your avian veterinarian for a consultation asap.
This amazon parrot was diagnosed with chlamydiosis. Notice how the wing isn't completely folded as it would normally be on a resting bird. The wrist of the wing is also very close to the birds ear, almost as if it was shrugging. The feathers on most of the body are fluffed up. This is very tired and sick bird.
Many species will use their feet to grab things when playing or exploring; especially young parrots that know each other well might even grab each others feet and "hold hands" while wrestling or playing. Birds can also put their feet up in many different situations. It can be a way to ask for some space, sort of like putting your palm up to say "stop, don't come closer." This is often seen in amazon parrots. Many tame parrots also put their feet up when they would like to step up, especially when they have a history of positive reinforcement for being on hands. It's also common for parrots to put one foot up or lightly scratch themselves when asking to be preened by another bird or person. In that context they will often have a relaxed body posture, fluff up the feathers on the head and neck, lower their head and bend their neck slightly.
This amazon is holding it's foot up. Notice how the bird is leaning slightly away from where it's looking? (If you look closely, you can se that the right side (from the birds perspective) of the tail feathers are slightly angled upwards. Also notice how the left leg and foot are not aligned.) This bird is also holding it's wings quite pressed against the body, has a lightly extended neck, and a very round eye. It is likely this bird was asking for some space while this photo was taken, but we can't know for sure without more information.
This galah (left) and blue and gold macaw (right) are holding their feet up as a part of preening or allopreening. Notice the relaxed and fluffed up head feathers, even weight distributrion, and loose body language. Parrots can do this to scratch themselves, or often as a way to indicate that they would like someone to preen or scratch their neck- and head.