Knowing when to use icons in your web design can make or break your UI.
Icons should achieve a single goal: communicate a message via a graphic that is universally understood by people. If an icon doesn't achieve this goal, then it's better to not use the icon.
The pro of using icons is that people process visuals faster than they read, particularly icons that are commonly used. For example, the phone icon has been around for ages and everyone knows what it means.
However, words are more reliable because they are specific. There are certain elements of web design where you will find yourself preferring words over icons, such as the navigation links in your navigation bar.