The awk utility maintains several variables as it processes a line of text from a file. As you already know, NR is the number of records that have been read from all of the input files. FNR is the number of records that have been read from the current file. When FNR is equal to 1, the condition portion of this awk statement is true and the action portion of the statement will be executed.
FILENAME is another variable maintained by the awk utility. It contains the name of the file that is being processed. You said your filenames were:

Code:

file001.txt
file002.txt
00000000011 character
12345678901 number within filename
file003.txt
...
file020.txt

The substr(string, start, count) function in awk returns count characters starting at character number start from string. For example when FILENAME is file001.txt, substr() will return the characters in red and store them in the variable fn (i.e., fn will contain the portion of the filename you want to print at the start of each line printed from this input file.
The awk printf(format, argument...) function is VERY similar to the C Language printf() function and the printf utility. In this case the function call:

Code:

printf("%s\t%d\t%s\t%s\n", fn, FNR - n, $2, $4)

prints the saved portion of the filename as a character string, a tab character, the current line number in the current file minus the number of lines in the current file starting with # as a decimal numeric string, a tab character, the 2nd field from the current line as a character string, a tab character, and the 4th field from the current line as a character string followed by a newline character.
You should use cut and paste when cut and paste do what you need to do and they do it more simply or more efficiently than could be done with your shell's built-in utilities AND you don't need more complex processing (such as that provided by awk or sed) that needs to be used to get the job done.

You should use cat when you need to concatenate two or more files into a single output file, when you need to feed the contents of one or more files into a utility that doesn't accept pathname operands, or when you have a version of cat that provides a non-standard extension that performs some text manipulation as it copies files that you need to perform.

You should NEVER use:

Code:

cat *.txt|awk 'awk program'

instead of:

Code:

awk 'awk program' *.txt

Creating an additional process like this takes more system resources to run your command, makes it run slower, and keeps awk from knowing how many files are being processed and what the names of the files are.

Many of the original UNIX utilities were designed to perform a transformation data read from standard input and write the transformed data to standard output. (These utilities can be called filters.) The idea was that filters could combined in a pipeline to perform much more complex tasks without making each utility more complex than needed. (This is an example of your basic KISS [Keep It Simple, Stupid] principle.) Unfortunately, many of today's utilities on many systems have forgotten the KISS principle.

Even with the original UNIX utilities, there were frequently many different ways to get a job done. Choosing which utilities to use depends on what you are trying to do, your ability to recognize the alternatives available, your ability to use the alternative tools available, and your knowledge of how utilities have evolved on various systems over the years so you know what will work portably on all of the systems you want to use and which code might have to be tweaked if you want to move your script to a different system.

Despite the fact that many of us have degrees in computer science or computer engineering (or both), there is a lot of art (as well as science and engineering) in programming.