When Mothra was first introduced, she was given an origin that suggested she was of divine lineage. She also had worshipers and two immortal fairy priests called the Shobijin who could communicate with Mothra telepathically over great distances. When the priests were captured and exploited, Mothra rescued them by devastating the city in which they were being held. Since that time, she has been featured in many kaiju films and has almost as many appearances as Godzilla over the decades. Her powers are huge blasts of air that can strike like typhoons, sticky web-like silk that's almost impossible to break, scales that can make it hard to breathe or even suffocate or which can form a shield to deflect energy blasts, and a radiant light that can really be anything from a peaceful bioluminescence to outright energy attacks on her enemies. It all kind of depends on who is writing Mothra at the time and what powers are called for in a battle (isn't that how these things usually go?).
I think that Mothra could communicate with other kaiju as well (definitely Godzilla) and the priestesses (the Shobijin I mentioned earlier) have facilitated this by communicating Godzilla's intent through Mothra to them and directly to humans around the Shobijin. I guess that's one way of getting your message across that you'd like your city to be spared if at all possible. Mothra, in a way, is kind of like a phoenix. There have been countless times when she dies battling a kaiju. But never fear, an egg has been left behind for her to hatch from at some point in the future (and to carry on with whatever it is that Mothra finds important). It's not necessarily a rebirth from the ashes kind of thing, but very close. And I'm not sure if the memories of Mothra actually get passed from one incarnation to the next. It seems likely, given the powerful psychic abilities that this particular kaiju demonstrates (it's the most powerful psychically gifted creature in the Toho monsterverse).
Anyway, as I'm writing this post on Thursday night before going to see Godzilla: King of the Monsters, I am hoping that the Shobijin make an appearance. However, there may not be room for that given that Millie Bobbie Brown's character seems to take up a lot of the human interaction with Mothra in the trailer. Maybe her character has psychic abilities similar to the Shobijin? Or maybe Mothra chooses her character as a priestess of sorts? Who knows? No matter how it goes, I think I'll still have a great time. How can you go wrong with classic kaiju and devastation porn to kick off a weekend?
I'll leave you with the newly updated score for Mothra that appears on the soundtrack for King of the Monsters. It was scored by composer Bear McCreary (who also did the theme for The Walking Dead).