Arachne was a very good weaver, but had a bit too much confidence as she claimed to be better than Athena, the Goddess of weaving herself.
I'm gonna win this
Athena, up in Olympus, heard this, and got very angry.
So Athena changed into human form and went to challenge Arachne
They both spent the day creating a massive tapestry, Arachne made one that mocked the Gods and Athena showed them as valiant.
Athena saw Arachne's tapestry and was shocked, she angrily turned into her Goddess form. Arachne was so shocked that she had not realised that she had just insulted a Goddess to her face. She ran off immediately and hanged herself.
Athena was so upset that Arachne had done this that, before Arachne died she changed the rope to a web and Arachne into a spider.