Updated: Apr 28, 2021
Hail to thee, Sekhmet, Queen of Heaven, Queen of the Two Lands, the Eye of Ra in his head, the Lady of Transformations to the head of he who begot her, the Eye of Fury, the Uraeus who is Master of Fear, the Queen of the Horizon! The Guiding Uraeus, the Daughter of great Ra, the Brilliant One, the Shining One, the Powerful One, the One Who is Power!... You are Sekhmet, who is at the prow of the Mandjet, Uadjet of the head of he who begot her.
--Hymn to Sekhmet-Bastet, Temple of Hathor at Iunet, ca. 1st century BCE
Sekhmet, Sam & Steph Braithwaite, 2014 for Hero's Journey
Sekhmet is the goddess of warfare, protection, and bloodlust, embodying both the dangerous and the positive outcomes of violence in one terrifying figure. Also called the Lady of Slaughter, she is the protector of the Pharaoh and leads Egypt's armies into battle, ruthlessly destroying all opposition. She is also considered to ride in the solar barque with Ra each day, protecting him from the forces of chaos and darkness that might otherwise plunge the world into darkness; between that and being Ra's daughter (or perhaps wife, or perhaps clone, depending on how you read the myth below), she's also obviously one of Egypt's many solar deities, usually appearing surrounded by blinding light and terrifying scorching heat.
Like so many Egyptian deities, her lion's head isn't just for scaring literally everyone who meets her. The lion represents not only physical power and merciless slaughter to the ancient Egyptians (it's one of their apex predators and the only one that you can't reasonably get away from by running to dry land) but also kingship and power, so for the goddess who is a terror to her enemies and the powerful right hand of her kings, it only makes sense.
The Eyes of Ra are upon you and they are very, very hungry
The stories of Sekhmet's exploits usually begin with her origin story, which is a lot like if someone dropped the xenomorph from Alien onto earth and let it go ham before instantly regretting all their choices. In the ancient days, Ra saw that humanity was disrespectful of him and others - the exact transgressions might vary depending on what priest from what area is telling the story, but it could be anything from killing each other to refusing to worship him to wrecking their landscape - and, as Ra often does, he becomes angry and starts talking about shutting down the universe so everyone can think about what they did. Hathor, his daughter, usually handles Ra in a funk by employing all her Goddess of Joy and Beer powers to cheer him back up, but she can't do very much about him being actively angry, and her powers just make humanity humanity that much harder.
So Hathor, the Eye of Ra and first of goddesses beside him, becomes Sekhmet instead. You can argue a lot (and the different cults of Sekhmet definitely do!) about whether she temporarily becomes Sekhmet and there's actually just one goddess who flips her aspect depending on the need, or whether she creates Sekhmet independently, or whether she tried to do the first one but the Sekhmet personality got away from her, but the bottom line is that Ra is now supported not by a gentle, beautiful, joyful goddess of getting blitzed and dancing under the stars but by a bloodthirsty, furious, unstoppable machine designed to woodchipper his foes first and never bother asking questions later.
And now Sekhmet is alive, so in very short order, most of the population of Egypt is not.
Not at all ominous to see looming out of the darkness behind you
Sekhmet's rampage is legendary, re-enacted by her worshipers now with colorful plays and rituals; she not only destroys the people who were offending Ra, but she goes on such a gruesome blood-soaked career of devastation across the landscape that the other gods start getting afraid of her themselves, and Ra realizes he's not going to have any people left to worship or not worship appropriately if someone doesn't stop her. (You can't really argue with her; no humans left definitely solves the problem of "some humans are being assholes", especially if you're thinking like a lion.)
Since she's legendarily bloodthirsty, they go with the obvious solution: pour blood into her until she's calmed down, except that the blood is actually beer dyed red so that she'll think it's blood, and the calming down is her eventually getting so smashed that she goes to sleep and the day is temporarily saved. It's neat that beer, heavily associated with Hathor who Sekhmet is/was/is a sister of, is also the vehicle that brings her back down from the violent stratosphere; just as Hathor needed Sekhmet to go do the violent parts, Sekhmet needed Hathor to bring her back to the everyday pleasures and joys of the rest of life.
Girls' Night Out: get a little drunk, eat a little of the Lower Kingdom, you know
Sekhmet's close identification with Hathor, her twin goddess (thus why she is often included in Hathor's temples!) who was too gentle to defend Ra from his enemies, has clear echoes with the Hindu myths of gentle Parvati manifesting the more warlike Durga and Kali in order to deal with violent foes. The two stories are coming from different theological standpoints - Hinduism considers all divinity essentially one and various deities and people as avatars of it, so it makes sense that a goddess can simply split off a new goddess with a useful set of powers as needed, whereas the ancient Egyptian religion considers all divinity mix-and-matchable and therefore can also manifest new goddesses as needed, just by taking the fighty bits from Deity A and grafting them onto some of Deity B - but they both come down to the idea that the goddess of violence and blood arises when she is needed to protect her people and gods. A nice parallel for Heroes who serve Sekhmet and are called by her, right?
Sekhmet also does a ton of other stuff, most of it the clawed murder of adversaries (for example, sometimes she might appear sawing Apep's head off or eating an enemy general who got too close to the Pharaoh), and she is also identified with her sister lion and cat deities, the collective Eyes of Ra, who include not just Hathor but also Bast, Mafdet, Menhit, Seret, Tefnut, Uadjet, and many more. Some followers of the Egyptian religion prefer to worship a single unified Eye of Ra that covers all of these goddesses; others treat each individually for their own powers and areas of influence. But even those who consider the Eye a single deity often acknowledge Sekhmet as the most powerful and dangerous of her facets.
Just trying to chill with your man but this Ramesses guy keeps inviting himself along
Sekhmet is usually considered the wife of the creator god Ptah, especially in his more powerful cult centers, where her undeniable power over violence and strife gives him a more commanding image to go with his usual powers over creation and technology. Explanation myths for this are more recent than most of her ancient lore, however; one popular modern-day myth is that Ptah was tasked by Ra to marry Sekhmet because he was afraid that without someone powerful watching over her at all times, she might rampage again, leading to some entertaining prayers to Ptah begging him to keep his wife from murdering everyone. Another is that Ptah and Sekhmet represent an important duality of creation and destruction that makes them perfectly complement one another (again, sounds like some divine Hindu couples we know about!).
In Hero's Journey, Heroes chosen by Sekhmet gain a little of her close connections to mayhem and the blazing sun, which they can then pass on to others. All the Egyptian Heroes get to choose partners among their fellow Heroes to connect with and share power between; in the case of one of Sekhmet's Heroes, they give their partners back Labors, allowing them to do more impressive feats, every time they use their own Labors on either the violent Warriors skills that their patron goddess so favors, or on Celestial powers associated with her heavenly domain.
In the end, Sekhmet represents almost pure Power. She is power, violence, force, energy completely unfettered by outside control or concerns. And in a religion where every deity has to help in the constant war against darkness and chaos, she's a really good goddess to have in their corner!