Aryen is an unspecified location in Temerant. It is likely the place where the trees which produce the rare and expensive roah wood are grown.
In the Chronicles
Aryen was where Graham had the wood shipped from to build the mounting board for Kvothe's sword, Folly. It took four months, with the roads being bad, for the wood to get from there to Newarre. 
The wood from Aryen is special in that it is incredibly hard and doesn't burn ; Graham said it was like stone under a saw and like iron when he tried to chisel it. After searing it with a hot iron for two hours, he said, the wood eventually turned black, and gave off a stink of old leather and clover, but didn't emit any smoke.
↑The Name of the Wind, Chapter 3, "Wood and Word" "He set the sword on the mounting board. Its grey-white metal shone against the dark roah behind it."