Muting emails in Gmail allows users to suppress notifications from specific conversations, making it easier to achieve inbox zero and reduce distractions. To mute an email, users can click on the "More" icon in the conversation menu and select "Mute", or right-click the email and choose "Mute". Muted emails are redirected to the All Mail folder with a Muted label, and replies to them bypass the user's inbox. Users can unmute emails by clicking the "Unmute" option in their All Mail folder or mobile app. Additionally, Gmail provides a search bar that allows users to find muted emails, and Zapier can be used to automate email-related tasks and connect with other apps.