There are two B&W technologies, traditional B&W process, and chromogenic.
in the case of the phrase you quoted, break it down thusly:
Leice M6 - the camera
TriX - the film, traditional B&W process
D76 - the developer
(1+1) the developer dilution
20°C the developer temperature
9min30 the development time.
Tri-X is a traditional B&W process film, the process is highly varied, a different developer, dilution, time or temperature can change the results, so it often means something. Especially if you know what your doing. The process has changed little in the last 150 years. Another advantage is that the process is very stable, there are glass plate negatives in existence from the 1800's that could as easily be printed or scanned now, as they could when brand new.
Chromogenic is similar to the colour process, except the dye clouds are black instead of coloured, has the advantage in that you can drop it at any lab for processing, the disadvantage is that the process is highly regulated, you can't vary the processing to get a different result. They have only been around for the last 20 years or so, we know that colour negatives from 30 years ago have faded, in some cases to a stand of not being usable. It's not be determined yet how long Chromogenic B&W films will last before they fade away.
The two processes are independent of one another, a film designed for one, should not be used with the other. Traditional B&W can be processed at home with a few simple tools, and some relatively inexpensive chemicals. A good place to start is the
Ilford Photo website
You can learn a considerable amount from there.