Exceedingly means to an unusually great degree, far beyond what's normal or expected. When something is exceedingly difficult, it's extraordinarily challenging, pushing beyond ordinary hardness. When someone is exceedingly kind, they go well beyond ordinary politeness.

Think of it as cranking something up several notches past the usual level. A test might be hard, but an exceedingly hard test pushes students to their limits. A room might be cold, but an exceedingly cold room makes everyone shiver and bundle up.

You'll often find this word in formal writing or when someone wants to emphasize just how extreme something is. “The mountain climb was exceedingly dangerous” tells you this wasn't your average hike. “She was exceedingly patient with her younger brother” means she showed remarkable, extraordinary patience.

Notice that exceedingly always intensifies another word. You wouldn't say “That was exceedingly” and stop there. You'd say “That was exceedingly clever” or “exceedingly rare” or “exceedingly fast.” It's a word that amplifies, turning ordinary adjectives and adverbs into something more powerful and notable.