Weaving is a craft to create a piece of fabric or cloth using yarn or thread. Athena is the goddess of weaving.
In The Mark of Athena, Annabeth Chase encounters several spiders, including Arachne herself. She tricks Arachne into weaving a tapestry by acting fascinated by her weaving and suggesting that she make it to decorate Olympus. Arachne falls for the trick and starts weaving. When Annabeth points out a "flaw," Arachne looks for the flaw and gets trapped in her own weaving.