Learn Spanish (Spain): La tienda está abierta.

We use está (from the verb estar) because being open is a state or condition. The shop's status changes between being open and closed. If we were talking about a permanent characteristic, like "the shop is big" (la tienda es grande), we would use es (from the verb ser).

Why is it abierta and not abierto?

In Spanish, adjectives have to match the noun they describe in both gender and number. Since la tienda (the shop) is a feminine noun, the adjective describing its state must also be feminine, so it ends in "-a" (abierta).

What would it mean if I accidentally said "La tienda es abierta"?

It would sound very strange! Because ser (es) is used for inherent characteristics, describing someone as abierto or abierta means they are an extroverted or open-minded person. Applied to a building like a shop, it sounds like a mistake. Always use estar for open or closed.

Is abierta related to the verb for "to open"?

Yes! The verb "to open" is abrir. Abierta is the adjective form created from that verb to describe something that is currently open.