What
"A collection of one or more test cases for the software under test"
BS 7925-1.British Computer Society Specialist Interest Group in Software Testing (BCS SIGIST)

Why?
We test for two reasons. Firstly to enable us to confidence, in behaviour of the software under test. Secondly to generate meaningful information on which we can make decisions. The Test Case suite enables the organisation to see and use a range of tests to exercise the software. Note, this does not necessarily mean exhaustively test the software.

The degree to which the test case suite is built into the test process, depends on the attitude to testing. Some organisations will have a formalized approach with lots of documentation. Others may use the opposite have an implicit acceptance. Typically this is posed verbally in the question "have you tested everything?"

Who?
Who is involved in the Test Case Suite depends on the organisation and may be project specific. Individual testers may take responsibility for ensuring "everything is tested". This would include deciding which areas to test, selecting cases, executing, logging and tracking defects.

Alternatively a formal structure may exist. For example a senior test analyst, might lay down guidelines on which features are to be tested. Junior analysts will actually select the cases. The test suite will then be executed either manually or with automated tools by test engineers or technician.

Where?
Anywhere the software is being tested. Thus from the developers own site through to the customer site.

When?
All phases or stages of the test process.

How?
The all important "How". If the organisation or project team have a very low ceremony approach to testing this section might be very short. The word of the tester, that everything has been tested, is sufficient.

In a very formal setup with a high level of ceremony, producing a suite of tests is a much more onerous affair.

A Test Design Specification may be drawn up following guidelines in IEEE829:1998. This will show which features are to be tested and how. The nature of the document is coarse grained. With greater granularity a test case specification is required for each test case. The test case suite and accompanying documentation may undergo a full inspection. Traceability will have to be shown from from each requirement. If a requirement is not fully tested then, this will have to be explained.

In reality most test case suites are produced between these two extremes. For example a document might be produced called the test spec. The spec does not conform to any recognised standard, but it does provide a record of the testing taking place and the tests undertaken.