By default, an avatar is displayed near the author’s name in WordPress comments. Its actually Gravatar. You may want to disable the WordPress avatar (Gravatar) for several reasons like to reduce server loads, keep the look of theme clean etc.
Its very easy to disable Gravatars in WordPress. Go to Settings > Discussion. Scroll down on this page to find the settings for Avatars.
Choose the option that says Don’t show Avatars and save the changes. That’s it. To enable avatars in WordPress again, just revert back the setting.