Honeycomb pieces are hollow hexagonal rings found throughout the levels in Gruntilda's lair, not to be confused with the full hexagonal honeycomb in the achievement picture which just restores your life.
There are 6 at the beginning tutorial of the game before the lair, and then 2 in each level. They are not TOO hard to spot, but if you havent played this game before, you'll most likely need to look them up in a guide.
6 of these pieces will permanently increase your life bar by an extra honeycomb, meaning you can increase your health by 4 whole honeycomb pieces by the end of the game.
UPDATE: Because the list links keep expiring, I've linked to a youtube video showing all the locations. Credit to whoever uploaded that video.
If you want a written list, you can search for a GameFaqs guide which isnt too hard to find on any search engine. I wont link to it due to permissions etc., OR you can see a solution posted below by a fellow TA member.