This use of the
も expresses completeness or totality, like the English word all. And in particular, when it's attached to an indefinite demonstrative (なに, どこ, どれ, だれ, どなた, and so on), it causes that word to refer to a complete set of the type denoted by the demonstrative:
だれも everyone (with positive verb)
だれも no one (with negative verb)
The same thing happens when you add も to other words like this:
どこも everywhere (with positive verb)
どこも nowhere (with negative verb)
どれも all (with positive verb)
どれも none (with negative verb)
But なに is an exception. It doesn't usually appear in positive sentences:
なにも everything (with positive verb)
なにも nothing (with negative verb)
So let's make things easier to understand by starting with an example that's not an exception. We'll use だれ, which means who, and we'll add も to that to make everyone. Here it is with a positive verb:
[ だれも ] が 知っています【しっています】
[ everyone ] knows
And now, with a negative verb:
[ だれも ] いません。
[ no one ] is here.
Why does the meaning change with a negative verb? Well, it doesn't really. The example above literally means "Everyone is not here", but the usual way to say that in English is with the logically equivalent "No one is here".
Okay, so now let's try a sentence with なにも. Like I said before, this is an exception, so we'll skip making a positive sentence and go straight to the negative:
[ なにも ] ありません。
[ nothing ] is there.
This literally means "Everything is not there". But again, that's not how we usually say it in English, so we translate it instead to the logically equivalent "Nothing is there". And your sentence is the same, except that it uses います (animate existence) rather than あります (inanimate existence).