Very important.

Your core is involved in almost every exercise you do. If you don't have a strong core, it can make exercises seem a lot harder than they should be.

If your core is not conditioned to be tight throughout your workout, you will struggle to maintain correct form from start to finish, and struggle to actually keep going.

Your core gives you stability, balance and power. The stronger and more trained your core is, not only will it be easier to make movements, but you will be able to use heavier weights too.