If I remember correctly, it means that there is enough sodium sulfide to react with all of the silver nitrate (plus some.) Basically, you don’t have to worry about the quantity of sodium sulfide, you can just assume all of the silver nitrate is used in the reaction.
If you were given quantities of both chemicals, you’d have to figure out which one would be depleted first, stopping the equation. That’s the limiting factor, and the other can be said to be in excess.
For example, if you have 2 units of A, and 3 units of B, and A and B react to form AB3 >> you get 1 AB3, and 1 left over, lonely, “excess” A. B was the limiting factor, and there was excess A.
In your case, you don’t have to worry about which depletes first—you’re given it already in the problem. Excess sodium sulfide. Silver nitrate is the limit.
I don’t remember enough of the details of this to give actual examples, hence “A” and “B” and “units.” Also “limiting factor” is probably not the technical term. But hopefully the concept comes across clearly enough?