"Tell me, Muse, the story of that resourceful man"
Here, Homer is asking for inspiration from Calliope, the Muse
of epic poetry. In Greek mythology, the Muses were the goddesses who provided inspiration for musicians, artists, philosophers, writers and other creative thinkers.
An invocation such as this was a traditional way for an epic poem to begin; the bard is asking for divine assistance in performing the story to as high a standard as possible.