Pith is the white spongy layer between citrus fruit and the peel. Hence, when a recipe calls for de-pith, it is instructing you to remove the white layer.
The pith of fruit has a very bitter taste to it that will affect the taste of marmalades, salads, desserts, etc.
How to de-pith
There is more than one way to de-pith fruit. You can either place the fruit on a cutting board and cut the peel and pith away with a sharp knife. Or you can use cooking tweezers like the video below. Either way, this method might take some practising and it might vary from fruit to fruit.
Watch How to de-pith below:
CLICK ON IMAGE TO PLAY