An integrated brim is a built-in ledge around the front of the helmet that shades your eyes from sun and helps channel rain and wet snow away from your goggles. It's a great feature if you frequently ski on bright, sunny days or in wet conditions where precipitation on your lenses is a constant annoyance.
This style is most common on all-mountain and freeride helmets, and it pairs well with those riding styles. The main thing to watch for is goggle compatibility — some goggle shapes don't sit quite right under certain brims, so it's worth checking the fit before you commit.
Keep in mind that a brim is primarily a comfort feature, not a safety one. It adds a small amount of weight and won't change how the helmet protects your head. If you mostly ski overcast days or prefer a cleaner, lighter look, going brim-free is perfectly fine.