What
"Testing of new features after regression testing of previous features." [Beizer]
BS 7925-1.British Computer Society Specialist Interest Group in Software Testing (BCS SIGIST)

See also the following techniques: Black Box Testing and Functional Test Case Design.

Why?
Simply because if we are adding new features to our software, we need to make sure that their behaviour as we expect. This is such an oxymoron, that most people would regard this as testing per se. Thus Progressive testing as a phrase, is heard much less than its opposite regression testing.

Who?
As progressive testing is all pervasive, everyone sooner or later will become involved. Either as a developer conducting small scale component testing or the customer user acceptance testing.

Where?
Again progressive testing will take place anywhere that the new features are to be exercised. This might be at the developers desk through to the customer site.

When?
In an ideal world, I suppose that we would follow Beizers definition. Thus we would make sure, that previously introduced features are still behaving properly, first. However in the real world, the temptation is to concentrate on the new stuff first. Regression testing is usually relegated to second place.

How?
As shown above, progressive testing is buried so far into the software quality cycle, it is difficult to pinpoint particular techniques. Far better, then to point to particular techniques on which to build. In addition to the ones above, see incremental testing and intergration testing.