In most cases the dimension is IP range - an automated process moves from IP address to IP address examining port 22 for any common vulnerabilities. Rarely do these processes check all ports. Moving your SSH deamon to a different port prevents those automated processes from then hitting your security layer on whichever port you are running.
The other dimension of attack is when an attacker is focusing on your IP address specifically. Then he probably is going to nmap your IP and discover which port(s) SSH is running on. Changing the default port for SSH doesn't help here, but this use case is far less common.
Like others have said, changing port doesn't remove the need for security measures (cert-based/passwordless login, disable root, fail2ban) but it reduces any of those even being tested in the first place when most of your attempted attacks are IP-range based.