Let us go back to your original code (with a space added between echo and $WORT and with the missing slash character added before dev/null ):
i=0
while read WORT
do
echo $WORT|grep a>/dev/null || echo $WORT|grep B>/dev/null || let i=$i+1
done
echo $i
You know what the first line does.
The read WORT reads the next line from standard input; removes the trailing <newline>; and, as long as the last character in the remainder of that line is not a backslash ( \ ) character, returns an exit code 0 which causes the while to run the code between the following do and done . If there the last character of a line was a backslash character, read will also remove the backslash character; read the next line from standard input; and append its contents to WORT recursively until a line is found that does not end with a backslash character. This continues repeatedly until an I/O error is encountered or an EOF is reached while reading from standard input. Either of these conditions will cause read to exit with a non-zero exit status causing the loop to be terminated.
Moving on to the grep commands inside the loop... The command:
echo $WORT|grep a>/dev/null
uses echo to write one line (after removing trailing backslash characters and merging lines) to grep a > /dev/null
The grep utility will read that line and if it contains one or more lowercase latin letter a ( a ) characters, it will copy that line to its standard output (in this case redirected to /dev/null ) and return success (i.e., a 0 exit status). Otherwise, nothing will be written to standard output and grep will return failure (i.e., a non-zero exit status).
In an OR-list (i.e.; a list of pipelines separated by the shell || operator, the 1st pipeline in the list is executed and its exit status is evaluated. If that pipeline succeeds, the OR-list is complete at that point; any remaining pipelines in the OR-list will be skipped; and the exit status of the OR-list will be success (i.e., exit code 0). If the first pipeline in the OR-list failed (i.e., returned a non-zero exit code), the next pipeline in the list is executed and its exit status is evaluated just like the 1st pipeline in the list. If no pipeline in the list succeeded, the exit status of the OR-list will be the exit status of the last pipeline executed. If any pipeline in the OR-list succeeded, the exit status of the OR-list will be success (i.e., 0).
An OR-list could also be written as a nested if statement. A nested if statement producing the same results as the OR-list in the loop in your code could also be written as:
if echo $WORT|grep a>/dev/null
then continue
else if echo $WORT|grep B>/dev/null
then continue
else let i=$i+1
fi
fi
As we can see from this (if it wasn't obvious when reading the OR-list n your code), this increments the value of the variable i for each line read from your script's standard input that contains neither a lowercase latin a nor an uppercase latin B.
Note that executing grep once or twice for each line in a text file containing lots of input lines is a slow and compute intensive operation. You haven't given us any sample input data and you haven't given us any indication of the sizes of the input files you will be processing, so we can only make wild comments about possible alternatives... For example, if your input files do not contain any continuation lines (i.e. lines ending with a backslash character immediately followed by <newline> character), your entire script could be replaced by a much simpler (and, for large files, much faster) single grep command:
grep -cv '[aB]'
If your input does contain continuation lines, your input files are relatively long, you want continuation lines to be merged into single lines before looking for the characters you're trying to match, you could still replace your script with an awk script that would join continuation lines (like read does when invoked without the -r option), look for the two patterns on joined lines and increment a count for lines that don't match either pattern, and print the count when it hits EOF on its input. (I'll leave writing this simple awk script as an exercise for the reader. With no description of the data that your script will be processing, there is no reason to waste the time writing a script like that if your input files will never contain continuation lines.)
I hope this helps you better understand what your script is doing.