In the case of fennel, the core is entirely edible, if a tiny bit firmer than the rest of the bulb. This means you can either leave it in or cut it out. Leaving it in will produce slices that each contain multiple layers of fennel, all held together by the core.
Do you eat the center of fennel?
Fennel will dry a bit after cutting, so if you need to cut it ahead, keep the slices wrapped in damp paper towels. The core is perfectly edible, and you can leave it if you like, but it can be a bit tough. I find that it's best to remove most or all of it when eating fennel raw.
Which part of fennel do you use?
All parts of the fennel plant—bulb, stalk, and the feathery fronds—are edible, and will add texture and flavor to salads, slaws, pastas, and more. Thinly sliced raw fennel bulb adds a sweet licorice flavor and crunchy texture to salads.