What does "Khorosho" mean?
What does “Khorosho” mean?


It's Russian: хорошо. 

I don't know Russian, so I can't claim to know how Russian speakers understand the word "khorosho", but I can tell you how Japanese speakers presume Russian speakers understand it. The Japanese understanding of "khorosho" is as an interjection used to express roughly "Wow!" or "Great!" or perhaps "OK." (cf. one, two, three). This appears to differ somewhat from how the word is understood by Russian speakers.

Understood as a fairly generic interjection, one can see why Eli/Alisa might have used it in the various contexts you point out in your question.


  And why wouldn't it be translated in the English subtitles?


I imagine it would've gone untranslated because it's a foreign word to Japanese viewers, too. 



Aside - for reasons that are not clear to me, "khorosho" appears to be Japan's favorite Russian word. The Japanese destroyer Hibiki was surrendered to the Soviets post-war (and renamed Verniy). Thus, Hibiki in Kantai Collection also frequently says "khorosho", because apparently that's just a thing that [Japanese people think] Russians do.