The term "Lead Alert" is a feature for automation (a.k.a. drip campaigns) that allows you to set a notification to an internal recipient.
Lead alerts are typically used to notify a sales rep of new contacts entering an automation or actions of contacts in a 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.