The term "Lead Alert" is an automated campaign that serves as a notification to an internal recipient.
Typically Lead Alerts are used in automation workflows.
Lead alerts can be used to notify a sales rep of new contacts entering an automation or actions of contacts in a workflow branch, like opened/clicked activity. (These are only a few examples, there are many more!)
Functionally, a Lead Alert is a physical email meant for an internal audience and triggered by some action in an automation workflow step.
Beyond automation, forms can be set up to send lead alerts upon form submission. In the form editor, click into the INFO tab