Volume Testing belongs to the group of non-functional tests

Non-functional tests

Non-functional testing is the testing of a software application for its non-functional requirements. The names of many non-functional tests are often used interchangeably because of the overlap in scope between various non-functional requirements...

, which are often misunderstood and/or used interchangeably. Volume testing refers to testing a software application with a certain amount of data. This amount can, in generic terms, be the database size or it could also be the size of an interface

Interface (computer science)

In the field of computer science, an interface is a tool and concept that refers to a point of interaction between components, and is applicable at the level of both hardware and software...

 file that is the subject of volume testing. For example, if you want to volume test your application with a specific database size, you will expand your database to that size and then test the application's performance

Performance

A performance, in performing arts, generally comprises an event in which a performer or group of performers behave in a particular way for another group of people, the audience. Choral music and ballet are examples. Usually the performers participate in rehearsals beforehand. Afterwards audience...

on it. Another example could be when there is a requirement for your application to interact with an interface file (could be any file such as .dat, .xml); this interaction could be reading and/or writing on to/from the file. You will create a sample file of the size you want and then test the application's functionality with that file in order to test the performance.