Everyday Carry, often shortened to EDC, is really just taking some care over the things you carry with you every day. To some, it's probably a little odd to make a minor hobby out of the stuff in your pockets, but caring a lot about the details of things most people don't give much thought to is something we can definitely relate to.
Usually, someone's EDC is based around a few nice quality items. These will usually include a penknife or small multitool, a pocketable torch, and often other things like a keyring, a wallet, and (the bit where we suddenly get more interested) a convenient way of taking notes wherever you are. The individual items tend to be quality things, usually metal so they'll stand up to plenty of use, often with an emphasis on things that will age well when they've been used for a while, so the whole kit will still look good in a few years.
You need to think about what will work for you - if you love fountain pens, a pocketable fountain pen, like the Liliput or our very own Cult Pens Mini, would be perfect. A ballpoint is always handy to have around, though, even if it isn't your usual preference. If your kit is modern in style, the Lamy Pico is a good choice - clicks down nice and short, but extends to a comfortable size for writing. A multifunction pen could give you a few more options without giving you more to carry, and if you really struggle to limit yourself, we have some nice and unusual cases to extend your pen carry a bit more than most!