Learn French: Le roi a découvert un grand gisement, d'où ces émeraudes. - The king discovered a large deposit, hence these emeralds.

You are right that d'où literally means 'from where' (as in D'où viens-tu ?). However, it is also frequently used figuratively to introduce the logical consequence or origin of what was just stated. In English, we use 'hence' or 'which explains' in the exact same way.

Why isn't there a verb after d'où?

When expressing a consequence, d'où is unique because it can be followed directly by a noun (in this case, ces émeraudes). You don't need a verb, although you could technically say d'où viennent ces émeraudes (from which these emeralds come). The verbless structure is very common and sounds elegant.

Could I use donc (therefore) or c'est pourquoi (that is why) instead of d'où?

You could use them to express the same idea, but you would have to change the grammar. Donc and c'est pourquoi must introduce a clause with a verb. For example, you would have to say donc il a ces émeraudes (therefore he has these emeralds). D'où is the only option here that works perfectly with just a noun.

What exactly is a gisement? Could I use it for a bank deposit?