Let's Encrypt is a free Certificate Authority (CA), and you can find out more details about them at https://letsencrypt.org
The API Let's Encrypt offers for certificate requests is known as ACME (Automatic Certificate Management Environment). Certify The Web is an ACME V2 client, which means it can talk to ACME Certificate Authority services which support the ACME V2 API.
Certificates issued by Let's Encrypt expire after 90 days, which means you need automated renewals to keep them active.
Every certificate renewal is a new certificate (not an extension of an existing one), with a new certificate thumbprint ('hash'). This means the certificate needs to be re-applied to whichever services were using the old certificate, which again requires automation.
The Certify SSL Manager app and related Certify The Web related services use the Let's Encrypt service to acquire free certificates and managed auto-renewal and (optionally) deployment.
There are many other tools and scripts available on many operating systems. We focus on providing a UI for Windows (and IIS in particular), to make the process as easy and quick as possible.