To monetize is to make money. If you write a popular blog, figure out how to monetize it so you don’t work for free. To monetize also means to establish a country's legal tender, as in to literally make money.
The word money hides in monetize because it’s all about money. Establishing a new currency, or printing money, is what happens when a country monetizes, like when the European Union decided to monetize the Euro as its new currency. This verb is sometimes used to mean "exchange for money.” These days, monetize often refers to figuring out a way to make money from a website or app.