An instance of Salesforce is the specific configuration that you see when you log into Salesforce. So my instance of Salesforce is what I see when I log in which is different from your instance when you log in which is different from what everyone else sees when they log in.
Salesforce instance refers to the server that your Salesforce organization lives on. ManySalesforce orgs (also referred to as an “instance”) live together on the same server, a method of server management called “multi-tenancy”. As opposed to one system living on one server, many instances live on one server.