The problem this solves

WordPress sends email by handing it to whatever the web server has arranged. On a lot of hosting that is nothing at all, so nothing is sent. On the rest it is usually a plain mail program with no sending reputation of its own — and because spam is sent the same way, receiving servers treat what it sends as suspect. The message is filed as spam, or accepted and silently dropped.

Nothing on the site says so. wp_mail() returns true, WordPress moves on, and the first anybody hears is a customer asking where their receipt went.

A mail service fixes it. It is a company whose whole business is being trusted by receiving servers — Gmail, Microsoft 365, SendGrid, and the rest. It authenticates your messages, keeps its own reputation clean, and tells you when something is refused instead of swallowing it. For the volume a normal WordPress site sends, most of them are free.