Computer
Refers to the server that hosts a SQL Server, this maybe a physical or virtual server.
Database
A database is a data structure that stores organized information. Most databases contain multiple tables, which may each include several different fields. For example, a company database may include tables for products, employees, and financial records. Each of these tables would have different fields that are relevant to the information stored in the table.
Instance
Also known as SQL Server or SQL server instance. SQL Server supports multiple “instances” or installations on the same host computer. Each instance runs independently from all others and has its own set of installation code, configuration parameters, system and user databases, memory allocation, and security configuration.