For most applications the inside of a bell pepper, the pale membrane holding all the seeds, needs to be removed. In my experience most home cooks do this by cutting the pepper in half, then scooping out the seeds with their fingers. Frankly this is barbarous: it’s a slow, clumsy method that will always leave seeds behind.
Your knife is faster and more fastidious than your fingers. Here’s a quick and thorough way to separate the core from the flesh.
Cut the top and bottom off the pepper.
Make a vertical cut through the wall of the pepper, then run your knife along the inside of the wall, like so:
In this manner you can quickly remove the core of the pepper in one piece without having to fuss over each individual seed. You also now have a perfect rectangle of crispy, juicy bell pepper that can be cut into uniform strips.
A visual summary of what we just did.
The stem of the pepper can be composted. The core has some flavour to it, and is most welcome in vegetable broths, especially those being used in corn chowder.