It was both a sign of her arrangement with her nearing end as well as of the desparation she probably wanted to hide with this little playing around. So I'd say she was just joking around a bit with him and trying to make some simple conversation, maybe even to supress the thoughts about her serious situation and her supposed end. So she was just happy to hear some human voice at the end of all hope (similar to user2176127's comment), be it just a remote man in Greenland (or wherever Aningaaq was from). She was at this point already preparing to die out there and was rather content with it. In addition to this she was out of fuel and without any hope to get home again. She reached someone on the radio, just to realize that it was an unkown man that couldn't understand a word she was saying. Well, I would say she was just drifting off a bit at this point. Even an incomprehensible muddled conversation is better than never having a conversation again. What the whole experience does to her mentality is unclear, but one possible role the scene plays is breaking her from a mood where she is resigned to her fate to one where the possibility of seeing earth again is worth fighting for. Stone also hears the sound of a baby crying, which she finds affecting. But it adds a strange atmosphere to the short account from his point of view. Stone obviously can't understand this part of the conversation.

The inuit is agonising about having to kill the dog as an act of mercy. The original howl was from an old dog now in severe pain. If you watch from Aningaaq's point of view another theme emerges. It's a little corny but it seems to work. During the conversation she encourages Aningaaq to make his dogs bark: she can't communicate effectively with the inuit, but dogs have a common language: she can howl at them, they can howl back. There is a tension between the human contact and the possibility it will be her last human contact. It may be her last chance to hear another person talk. But she does get to hear another voice before she is doomed to die. She has finally been able to contact someone, though they can't really communicate. I'd say that the key theme from Stone's point of view is the balance between hope and despair.

Some are more apparent if you watch the conversation from Aningaaq's side which, amazingly, was filmed as an add-on to the movie by Jonas Cuaron (son of the director and co-writer).

There are many things symbolised in the radio conversation with Aningaaq (an Inuit somewhere in the middle of an arctic wilderness).

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