Quoting means just that, bracketing a string in quotes. This has the effect of protecting special characters in the string from reinterpretation or expansion by the shell or shell script. (A character is "special" if it has an interpretation other than its literal meaning. For example, the asterisk * represents a wild card character in globbing and Regular Expressions).
bash$ ls -l [Vv]* -rw-rw-r-- 1 bozo bozo 324 Apr 2 15:05 VIEWDATA.BAT -rw-rw-r-- 1 bozo bozo 507 May 4 14:25 vartrace.sh -rw-rw-r-- 1 bozo bozo 539 Apr 14 17:11 viewdata.sh bash$ ls -l '[Vv]*' ls: [Vv]*: No such file or directory
Certain programs and utilities reinterpret or expand special characters in a quoted string. An important use of quoting is protecting a command-line parameter from the shell, but still letting the calling program expand it.
bash$ grep '[Ff]irst' *.txt file1.txt:This is the first line of file1.txt. file2.txt:This is the First line of file2.txt.
Note that the unquoted grep [Ff]irst *.txt works under the Bash shell. 
Quoting can also suppress echo's "appetite" for newlines.
bash$ echo $(ls -l) total 8 -rw-rw-r-- 1 bo bo 13 Aug 21 12:57 t.sh -rw-rw-r-- 1 bo bo 78 Aug 21 12:57 u.sh bash$ echo "$(ls -l)" total 8 -rw-rw-r-- 1 bo bo 13 Aug 21 12:57 t.sh -rw-rw-r-- 1 bo bo 78 Aug 21 12:57 u.sh
Unless there is a file named first in the current working directory. Yet another reason to quote. (Thank you, Harald Koenig, for pointing this out.