What is SSH? How to check if a Linux server is running SSH?

Wikipedia Definition: "SSH or Secure Shell is a cryptographic network protocol for operating network services securely over an unsecured network."

Hostinger.com Definition: "SSH, or Secure Shell, is a remote administration protocol that allows users to control and modify their remote servers over the Internet."

An SSH server will have SSH daemon running. Depends on the distribution, you should be able to check whether the service is running (e.g. systemctl status sshd).