What does "running to stand still" mean?

I have some questions about these sentences.

We are a culture more sexualized than ever (Mad Men notwithstanding), with technology that’s made it easier than ever to “better” ourselves, warping our standards for what’s normal. Plastic surgery used to be for the rich and famous; today we’ve leveled the playing field with cheap boob jobs, tummy tucks, and outpatient procedures you can get on your lunch break. Where that leads us is running to stand still: taught that good looks are no longer a gift but a ceaseless pursuit. (from a Newsweek article)

What does “running to stand still” mean in this context? And what is “taught” grammatically?

It means that we make a lot of effort (we “run”) to look more attractive than other people but we end up looking plain because everybody has done the same (“we stand still”), so we must make more and more efforts (“a ceaseless pursuit”)
You can use that expression in any case in which something similar happens.

“Taught” = “We are taught”, so it’s a participle.

Thank you, ftornay. Now I understand.