I like to remember it like this:

energy = work + heat

And work is 0 at constant volume because work = pressure x change in volume.

Heat capacity is a measure of energy on a per mass (or mole) and per temperature basis. But it's basically a measure of ENERGY. So, if you're at constant volume... there's no work! Less energy is required. If you're at constant pressure, work can be done, so more energy!

Let me know if that helps. 😁