What is an SMTP relay and when do you need one?
An SMTP relay is a service that sends your application's mail, instead of sending it from your own server.
Why you need it
A web server usually has no sender reputation at all. Mail sent straight from it lands in spam or is refused, however good your message is.
What it gives you
Correct authentication, IP addresses with a maintained reputation, delivery reports and bounce handling. Above all you get visibility into what actually happens.
When you need one
As soon as an application sends mail automatically: order confirmations, password resets, notifications, invoices. Which is nearly always.
What changes at your end
A host, a port and credentials in your application's configuration. Technically it is a small change.
What you must arrange
Add the relay to your SPF and enable DKIM for your domain. Without that you have moved the problem rather than solved it.