Matcha is sensitive to light, heat, and humidity. It oxidise quickly, so proper care is imperative. For home storage, you should avoid clear glass containers or leave matcha in direct sunlight for this reason.
Most matcha comes in a tin, once opened, it's hard to keep it away from the moisture in the air. Proper storage will extend the bright green colour, umami taste, and silky texture are preserved in every serve.
Refrigeration is a point of debate; some say it preserve freshness, personally I'd never store matcha in a fridge, as it can introduce too much moisture and easily absorb the smells too.