LC_ALL is the environment variable that overrides all the other localisation settings (except $LANGUAGE under some circumstances).
Different aspects of localisations (like the thousand separator or decimal point character, character set, sorting order, month, day names, currency symbol) can be set using a few variables.
You'll typically set $LANG to your preference. The individual LC_xxx variables override a certain aspect. LC_ALL overrides them all. The locale command, when called without argument gives a summary of the current settings.
For instance, on a GNU system, I get:
$ locale
LANG=en_GB.UTF-8
LANGUAGE=
LC_CTYPE="en_GB.UTF-8"
LC_NUMERIC="en_GB.UTF-8"
LC_TIME="en_GB.UTF-8"
LC_COLLATE="en_GB.UTF-8"
LC_MONETARY="en_GB.UTF-8"
LC_MESSAGES="en_GB.UTF-8"
LC_PAPER="en_GB.UTF-8"
LC_NAME="en_GB.UTF-8"
LC_ADDRESS="en_GB.UTF-8"
LC_TELEPHONE="en_GB.UTF-8"
LC_MEASUREMENT="en_GB.UTF-8"
LC_IDENTIFICATION="en_GB.UTF-8"
LC_ALL=
I can override an individual setting with for instance:
$ LC_TIME=fr_FR.UTF-8 date
jeudi 22 août 2013, 10:41:30 (UTC+0100)
Or:
$ LC_MONETARY=fr_FR.UTF-8 locale currency_symbol
€
Or override everything with LC_ALL.
In a script, if you want to force a specific setting, as you don't know what settings the user has forced (possibly LC_ALL as well), your best, safest and generally only option is to force LC_ALL.
The C locale is a special locale that is meant to be the simplest locale. In the C locale, characters are single bytes, the charset is ASCII, the sorting order is based on the byte values, the language is US english and things like currency symbols are not defined.
On some systems, there's a difference with the POSIX locale where for instance the sort order for non-ASCII characters is not defined.
You generally run a command with LC_ALL=C to avoid the user's setting to interfer with your script. For instance, if you want [a-z] to match the 26 ASCII characters from a to z, you have to set LC_ALL=C.
On GNU systems, LC_ALL=C and LC_ALL=POSIX (or LC_MESSAGES=C|POSIX) override $LANGUAGE, while LC_ALL=anything-else wouldn't.