What does the objective "kill 4 nones" mean?

It's possible that this is some sort of glitch, more specifically a null pointer error, as there is no such entity named "None" in Fallout Shelter or the Fallout universe in general.

In many languages a mistake could be made in the code which causes an 'object', such as the name of an enemy you need to kill, to end up being nothing or null.

Some languages such as Python and possibly others use the notation None instead of null.

Likely there is also code that attempts to make the object plural if you have to kill more than one so None gets an s appended to the end.

This is possibly why you are getting that being displayed.

It's possible that this is still achievable, but it is unlikely and I'd recommend skipping it.

Unless you are particularly keen on testing, I'd suggest skipping that Objective. There is a very high chance it is something that didn't get added or is intended for a future update. As such there is probably very little chance of accomplishing it unless it turns out that "Nones" was supposed to be Molerats or Deathclaws and just didn't get changed when they were added. I doubt that this is accomplishable.