WHY IS MAMBWE DISTRICT OF EASTERN ZAMBIA NOT SHOWING?

I guess Mambwe is in the data if you are referring to this district. It's just that map makers have to select features they show or not show. Not everything can be shown on a map, it would become far too cluttered up. Map makers of the map on www.openstreetmap.org have decided not to render amininstrative entities of admin level 5 to which Mambwe belongs. You might find other maps that do display the disctrict.

Because nobody has added it?

OpenStreetMap only contains data for features that somebody has found worthwhile to add, and it seems that in this case nobody has. Further because administrative boundaries are difficult to survey, typically they are imported from third party sources that have licence terms that are compatible with OSM. If no such source exists then it is unlikely that such information can be added in a reasonable manner.