Can it be summarized for lay persons in 25 words or less?

Probably not. I can't get it to load so I'm not sure what the article says exactly. But I can guess, as I know a fair bit about her contributions to both mathematics (hopeless to summarize for non-mathematicians) and physics (for which there's more hope, but not in 25 words or less).

An interesting anecdote about Noether: I believe she earned her PhD from the University of Gottingen (I think the first woman to do so in mathematics, maybe in any field). The mathematics faculty wanted to keep her on as a faculty member, but this was unheard of -- women could not be professors. So, for a while, before she moved to the States and took a position at Bryn Mawr, David Hilbert signed up to teach extra courses, had Noether teach them, and passed the extra pay to her under the table.