So basically a core is a group of 2-3 Pokemon that work (well) together, and usually are the most important part of/do the most work on the team.
Preparing for individual 'mons in the team building phase is one thing, but more important than that is preparing for cores of Pokemon. So in the interest of helping people build teams a little better, what are some of the most commonly used cores in today's metagame? In this game you can't prepare for literally everything, but Pokemon is no different from any other game with a competitive scene in that certain characters or groups or teams are far more common than others. Preparing for what's common will do a lot for you.
Some Drunk Scottish Betch
"Me maw gets so jel wen ay do anythin fun, like no my fault am out snortin lines n shaggin nines nd ya have ta stay home an bake a lasagne."