how would you explain ppc management to a client?

I usually say: you pay every time someone clicks your ad, and my job is making sure you're paying for the right clicks. Then what that means in practice. Picking keywords, writing the ads, blocking searches that waste money, adjusting bids and budgets, and reporting what each dollar brought back. It lands faster with their own numbers. "Last month you spent X, got Y leads, each lead cost Z" works better than any definition.