Too long for a comment, but indeed as already answered (please vote up)
1. a wildcard DNS *.wordpress.com.
record so that you don't need to actually create a new DNS record, a new subdomain, for each new subscriber.
2. A similar pre-installed wildcard SSL certificate valid for *.wordpress.com.
so that all potential subdomains automatically already have TLS support and there is no need to generate and install a new SSL certificate for each new subscriber either.
3. A web site / web application that is designed for multi tenancy. For each new subscriber only a new profile gets created and their "own" customised WordPress site becomes active immediately, without having to install, deploy, configure and customise a copy (or an instance) of the (stand alone) web application.
This leverages the fact that for HTTP/HTTPS the web browser must send a Host:
header with each request containing the DNS hostname of the website the visitor wants to visit. That allows the server back-end to select if a subscriber using that subdomain exists and then show the pages for that particular WordPress site.
When visiting a subdomain which hasn't been claimed yet by a subscriber, the server backend will typically take you to a sign-up page.
(For background see the name based virtual hosting and for TLS the Server Name Indication wikipedia articles.)