Layman's breakdown:
The facts of the case.
Ames had a job. Her performance reviews were generally positive. Her manager was gay, and Ames is straight.
She applied for a promotion. She didn't get it. Another person was hired for the promotion, who was gay.
Ames was demoted to a significantly lower paying job, and someone else was hired for her previous role. That other person was also gay.
She sued for discrimination based on sexual orientation.
The established precedence for testing discrimination has three steps. The first step is establishing that something fishy happened that may have been discriminatory. This is ostensibly a low bar to entry to a lawsuit. You just have to demonstrate something happened. Like, you can't sue for "they looked at me funny" or "they didn't like me because I'm [fill in protected class]." You don't have to prove that you were the victim of discrimination at this level, you just have to demonstrate that there is something that requires review.
This is called the McDonnell Douglas burden shifting framework, and the next step is that the business has to prove there was a legitimate business reason for the something that happened. You can see why the first step is a low bar but also an important step. If the case is "they looked at me funny," how is the business supposed to defend against that? "You had a weird hat on," or simply, "that's just my face." If there's an obvious business explanation, then the third step is it goes back to the complainant to demonstrate that the business reason is discrimination or bullshit.
It's a reasonable framework that ensures all discrimination allegations are handled consistently and methodically. The court doesn't jump into whether weird stares are discriminatory or not until after they have determined that there's something to evaluate and the business has had a chance to justify it.
An example could be a waiter suing Hooters for gender discrimination because they didn't hire him. The first step is that the restaurant did not hire him and hired someone else, a woman. The next step is the restaurant justifying the business decision, that the restaurant's business model is built on women's boobies, so they exclusively hire waitresses. The third step is the waiter trying to prove that the business decision is discriminatory, and that a man could have boobies as profitable as a woman.
So Ames presented her case, but the lower appellate court required that Ames additionally demonstrate that her employer had a history or pattern of discrimination against straight people. The thought process was that "reverse" discrimination against straight people is relatively rare, so to pass the first step, Ames needed to meet an additional burden. Notice how many times I said "additional"? That's not how laws are supposed to work. The framework never got to the second step in the process because the court applied a different standard to the complaint. The court had a legal reasoning for this, but anyone following the case knew that it was a decision that would not survive on appeal.
The SCOTUS sent it back down to the lower court to apply the standard framework, which Ames will still probably lose. It's really hard to demonstrate discrimination, especially when the people making the decisions were also straight. Mediocre performance reviews are not a strong case that you deserve a promotion, and she accepted the demotion rather than sue for constructive dismissal. It's hard to say that she will win her case, but it's a bit alarming how well-funded her legal team seems to be.
Even more alarming is the concurrent opinion by Thomas and cosigned by Gorsuch essentially admitting that they don't like the McDonnell Douglas framework and would overturn the precedent if that was the question before the court. Maybe it isn't a perfect framework, but the oligarchs that own the conservative justices clearly have a target in mind, and are basically colluding with the complainant to come back with a different argument that would allow conservatives to eliminate some additional human rights.
So those are the objective facts of the case. Anything more would be speculation.