Which of the following is a primary function of adware?

Adware is primarily designed to display advertisements to users. It generates revenue for its developers by installing itself on a user's computer and showing ads, often in the form of pop-ups or banners, while the user is browsing the web or using software. This form of software typically comes bundled with free applications, making it a common way for developers to monetize their products. The advertisement display is often tailored to the user's interests based on their browsing behavior, which can lead to targeted advertising.

The other options do not align with the main function of adware. Enhancing network security pertains to antivirus or firewall software, running background checks on users relates to surveillance or user tracking software, and optimizing software performance involves applications aimed at improving system efficiency. Each of these functions serves a very different purpose than that of adware, reinforcing the fact that adware's central role is to deliver advertisements.