Many people passively review their analytics at the end of the week or end of the month (if at all!) This may be too late to see and respond to something that changes. If you only log in to look at the numbers occasionally you may be missing important information at a critical time. Alerts allow you to be notified on a daily basis whenever some criteria is met (for example, when traffic sessions decrease by more than 10% from the previous day.) You can thereby know about changes right away, investigate the cause, and respond to it.
You can set up alerts to notify you by email or text message to your phone, so you will always receive them when needed.
To set up your alerts, go to Intelligence Events -→ Overview -→ Custom Alerts OR Admin → Custom Alerts under the site view that you want to monitor. You can then create a pattern match for whatever you want to be notified about. The patterns can match pretty much anything that GA can track. Think of what matters to you and set up as many or as few as you need. Monitored scenarios should be those that you are interested in but which are out of the ordinary so that you do not get flooded with alert messages.
Google Documentation: Create and manage custom alerts