Mama Killa is the Moon Goddess in the Incan religion and one of many Moon Deities that was truly considered to be the embodiment of the moon itself. Thus, in a culture that followed a lunar calendar to know the passing of time, Mama Killa found herself no shortage of devotees.
One thing about gods and goddesses truly considered embodiments of celestial bodies is that they create even more concern and explanation of the physical phenomena caused by said body in the sky. Here, in Incan culture you see many myths associated with these lunar traits and happenings.
One myth is a common one in subject matter across countries and cultures around the world. Eclipses were always concerning for early humans and thus, we created many stories and rites to deal with this. The Inca would create massive amounts of noise, make gestures and throw weapons during the Lunar Eclipse, in order to scare away the animal they saw this event bringing to pursue Mama Quilla.
Another story that is told one of a few ways over time came about to explain the uneven countenance of the moon. In one telling, She meets a fox that is enticed to fall in love with her because of her beauty. When he gets there, she embraces him so close that it causes the dark patches we see. Alternatively, you can also find tellings in which her brother/husband the Sun gets jealous of her light and beauty and causes the patches by throwing hot ash in her face. This, interestingly enough, is a regular thing across moon myths. Often, the lunar god is described as being brighter at first and will gamble away its light, or have it taken through jealousy.
So, while Mama Killa was worshiped almost exclusively by women, she was a Goddess of great importance for everyone. When it came to protecting her during the eclipses, which they thought of as having her in peril, everyone took part in order to protect what they thought was something that could always.