Web performance refers to how quickly site content loads and renders in a web browser, and how well it responds to user interaction and that directly impacts conversion rate.
Conversion rate is the percentage of website visitors that do something on the site that serve the goals of an organization or business, for example, if 100 users visit the page advertising some product, and 2 users actually click the 'buy' button, the conversion rate is 2%.
According to an Portent research in 2019, the highest e-commerce conversion rates occur on pages load times between 0-2 seconds, spanning an average of 8.11% e-commerce conversion rate at less than 1 second, down to a 2.20% e-commerce conversion rate at a 5 second load time. After that, conversion rates are largely below 2% (except for the 7-second anomaly, which briefly returns to 2.11%).
Performance plays a major role in the success of any online venture. High-performing sites engage and retain users better than low-performing ones. Pinterest reduced perceived wait times by 40% and this increased 15% in SEO traffic and 15% percent in conversion rate to signup.
But you should not look at data from others and trust the same will apply to your site. You should analyze your own data and set your own goals. In this Web.dev article they show how to relate site speed and business metrics.
Besides conversion rate, engagement and traffic, there are others things that have great benefits from web performance like accessibility, empowered user experience, metrics and objectives that are key results to the organization business, and this is why you should care about web performance.