The protagonist is so cold that he can't strike a match using his frozen hands, so he's managing it with his teeth. He needs to separate one match from the bunch of matches, again using his teeth. In order to do this, he's baring his upper teeth by moving his lower jaw and upper lip out of the way: he "drew the lower jaw in" (meaning "in" towards his body) and "curled the upper lip out of the way". The posture of his jaws is then somewhat like the rightmost of the following pictures (although due to stretching himself rather than the natural shape of his bones, and with his mouth open too):
By drawing his lower jaw in (backwards towards his body) and curling his upper lip up, he's able to bare his upper teeth and use them to separate one match out of the bunch.
As a side note, there are at least two versions of the text of this story. One version has the passage in the way that you quoted it, while another version has a much less descriptive version:
After some struggling he managed to get the pack between his mittened hands. In this manner he carried it to his mouth. The ice broke as he opened his mouth with a fierce effort. He used his upper teeth to rub across the pack in order to separate a single match.
The Wikipedia page mentions two versions, from 1902 and 1908, but both of the above-linked versions have the ending of the 1908 story rather than the 1902 one, so apparently there are at least three versions of the text.