The core of a fruit is the central part of it. It contains seeds or pips.

If you core a fruit, you remove its core.

The core of an object, building, or city is the central part of it.

The core of something such as a problem or an issue is the part of it that has to be understood or accepted before the whole thing can be understood or dealt with.

A core team or a core group is a group of people who do the main part of a job or piece of work. Other people may also help, but only for limited periods of time.

In a school or college, core subjects are a group of subjects that have to be studied.

The core businesses or the core activities of a company or organization are their most important ones.

You can use to the core to describe someone who is a very strong supporter of someone or something and will never change their views. For example, you can say that someone is Republican to the core .

If someone is shaken to the core or shocked to the core, they are extremely shaken or shocked.