What is the goal of a paid search campaign?

The goal of a paid search campaign depends on what the campaign is built to do. A bottom-funnel conversion campaign exists to capture active demand: someone is searching for a solution and the campaign's job is to get them to a landing page that converts at an efficient cost per acquisition. A brand defense campaign has a different goal, which is to prevent competitors from buying your branded search traffic and making customers second-guess you on their way to your site. A competitor conquest campaign aims to put your ad in front of people searching for a competitor, with the goal of pulling consideration your direction. A demand capture campaign inside a full-funnel Google Ads program is designed to convert the buyers that upstream demand generation has already warmed up. Treating "paid search campaign" as a single type of campaign with a single goal is a common reason paid search programs fail. The real goal is whatever specific commercial outcome the campaign was designed for, and the measurement has to match.