¿Mande?

When somebody just talks to you and you don't catch what was being said, what do you say?
"Excuse me?"
"Pardon?"
"Could you say that one more time?"
etc., etc.

but not something like "Your order?" though?

However, if you're in Mexico, that's what people often say when they didn't hear what you said the first time. "¿Mande?" which means roughly "Your order?" kinda like "At your service, sir/ma'am."

The explanation I got from somebody (I don't remember specifically who by now but a Mexican) was that when the Spaniards took over, they killed the local people at the slightest mistakes, so the local people could not admit that they did not understand what was said to them, bothering the Spaniards with having to repeat themselves.

This was the explanation also given to me for why things never get done on time in Mexico. If you ask for a service, even if they are not able to fulfill your request the way you want it, they can't say no. That would have been another death sentence from your Spanish Lord. Or maybe it's just a face-saving thing, where you can't admit that you lack the resources or capabilities to do your client's bidding. That would bring shame. Partial or late fulfillment is better than an outright refusal.

I don't know how true this interpretation is, but the fact that such an explanation exists reflects the tragedy of what the Europeans did to native Americans.

Now "Mande" is just a saying embedded in the context. Even among people who are on tutear (peer) terms, they don't conjugate it to "Manda." It's still third person singular (honorific), "Mande."