Adding eggshell to the grounds of coffee is said to take away some of the bitter taste that can be associated with cheap or over extracted coffee. The eggshells are typically cleaned after making eggs and allowed to dry, then simply added to the drip coffee filter where the coffee grounds go.
Alternatively, they can also be added to a fresh press before depressing the plunger, but may slow down the press.
People also use eggshell to settle the grounds of the coffee.
It's an old practice dating back to the early 1900s (and earlier) and I believe this to be fairly rare now.