In table top role playing games core books are the book or books considered necessary to play the game. Starting from the grand daddy of all RPGs, D&D, it was assumed from Advanced onward that players would have access to the Player's Handbook and Dungeon Masters would have access to both the Dungeon Master's Guide and the Monster Manual. These three pillars have persisted to the present edition more or less unchanged. Despite this, most games have a single core book meant to be the fully self contained game. This is highly effective from a simple marketing/sales perspective as consumers can just buy and run games straight from the book without discovering that they are missing parts. The other major method is to create separate Players and Game Masters guides. This makes sense from a basic resource division stand point. Three hundred pages for players and two hundred pages for GMs all crammed into one book makes for a pretty weighty and expensive tome. Splitting them brings down the cost of entry for new players without taking away anything they need to play.
In my experience core books always have at least two parts: character creation and resolution mechanics. Who and do. Without these there really isn't a game. Most will also include an equipment list, setting info when applicable, suggestions on tone, and sometimes an introductory adventure. All of these facilitate entry into the weird and hopefully wonderful world of whichever table top game you happen to have the book(s) for. It's worth noting that many systems make their core books free or very cheap to tempt people into trying the system. Others create free, truncated versions of their core rules typically called "quick starts" that provide a super simplified version of the rules. Obviously, this is exclusive to digital distribution since the cost of hosting PDF files is basically zero unlike printed paper copies.
IRON NODER XIV: THE RETURN OF THE IRON NODER