Arms can act as the doorway to the body and the self. When they are crossed, they form a closed defensive shield, blocking out the outside world. Shields act in two ways: one is to block incoming attacks and the other is a place behind which the person can hide and perhaps not be noticed.
Crossed arms may thus indicate anxiety which is either driven by a lack of trust in the other person or an internal discomfort and sense of vulnerability (that may, for example, be rooted in childhood trauma).
The extent of crossing indicates how firmly closed the person is. This may range from a light cross to arms folded to arms wrapped around the person. An extreme version which may indicate additional hostility is a tight close with hands formed as fists. If legs are crossed also then this adds to the signal.
The hands in an arm-cross may also be used to hold the person in a reassuring self-hug, for example holding upper arms in a folded-arms position or wrapped around the torso, holding the sides. If the thumbs are up, this may indicate some approval or agreement with what is being said.
Crossed arms, especially when holding one another can show the person to be trying to keep themselves still. This can be to suppress any signals. It may also indicate repressed anger (I have to hold myself to prevent myself hitting you). In some cultures it also signals that the person is holding themself still so they can pay greater attention to you (and is hence a compliment).
When arms are not crossed, they expose the torso and the person, making them more vulnerable. This signifies comfort that often indicates trust. It can also be power position that dares the other person to attack whilst knowing that the other person dare not.
Crossed arms is a very obvious signal and if you do it in front of other people they will likely feel rejected and respond accordingly (including not agreeing with you).
Note that not all crossed arms are defensive. Sometimes folded arms, for example, are just a relaxed position. Crossed arms are also used when the person is cold (this is typically done with hands tucked under armpits to keep them warm).
A common method sales people use to break a crossed-arms closed position is to give the person something to hold or otherwise ask them to use their hands.
