Recap: The muses are the nine daughters of Mnemosyne, the goddess of memory. They bring inspiration to artists, musicians, dancers, and authors: basically anyone who works with "the arts." While Minerva is visiting with them, they tell her a story of nine mortal sisters who challenged them to a singing contest. When the muses won the contest they transformed the sisters into birds as punishment. Their story reminds Minerva of rumors about Arachne.
The Muses aren't actually in this story. We mention them as background information that helps to make the story easier to understand. You see, Ovid (the dude whose book we used for the summary) has a tendency to start his stories right at the tail end of whatever story came before. In this case, Minerva Visits the Muses is the story that comes right before Minerva and Arachne. The first few sentences of Minerva and Arachne refer back to Minerva's visit, and this can be confusing if you haven't read that story. Aren't you glad we're here looking out for you? Yeah, we thought so.