Part of the following is taken almost verbatim from the Fourth Edition of George Grätzer's More Math into LaTeX:
LaTeX places a certain size space between words—the interword space—and a somewhat larger space between sentences—the intersentence space (as required in
English typography). To know which space to use, LaTeX must decide whether or not a period indicates the end of a sentence.
To LaTeX, a period after a capital letter, for instance, A., signifies an abbreviation or an initial. Generally, every other period signifies the end of a sentence.
This rule works most of the time. When it fails—for instance, twice with e.g.—you need to specify the type of space you want, using the following two rules.
Rule 1
If an abbreviation does not end with a capital letter, for instance, etc., and it is not the last word in the sentence, then follow the period by an interword space (\ ) or a tie if appropriate. Recall that \ provides an interword space.
\documentclass{article}
\begin{document}
\noindent The result was first published, in a first approximation,
in the Combin.\ Journal. \\
The result was first published,
in a first approximation, in the Combin. Journal.
\end{document}
prints as
Notice that "Combin." in the first line is followed by a regular interword space. The intersentence space following "Combin." in the second line is a little wider.
A tie (or nonbreakable space) is more appropriate than \ in phrases such as Prof. Smith, typed as Prof.~Smith, and pp. 271–292, typed as pp.~271--292.
The thebibliography environment handles periods properly. You do not have to mark periods for abbreviations in the name of a journal, so
Acta Math. Acad. Sci. Hungar.
is correct.
Rule 2
If a capital letter is followed by a period and is at the end of a sentence, precede the period with \@. For example,
\documentclass{article}
\begin{document}
\noindent follows from condition~H\@. We can proceed\\
follows from condition~H. We can proceed
\end{document}
prints:
Notice that there is not enough space after "H." in the second line.
To make all intersentence spaces equal to the interword space—as required in
French and Spanish typography—you can use the command
\frenchspacing
To switch back to using spaces of different sizes, give the command
\nonfrenchspacing
Addressing now the specific question, the \@ command must be used to generate the correct kind of space in the cases in which LaTeX mechanism fails; if \@ is used to the right of a dot, it prevents extra space from being added (the dot will not be considered as a symbol ending a sentece). If \@ is used to the left of a dot, it tells LaTeX to interpret the dot as a symbol ending a sentece.
Let's take a look at your concrete example; let's compare the result of:
\documentclass{article}
\begin{document}
\noindent blah blah word WORD. Next sentence \\
blah blah word WORD.\@ Next sentence \\
blah blah word WORD\@. Next sentence \\
blah blah WORD word. Next sentence \\
blah blah WORD word.\@ Next sentence \\
blah blah WORD word\@. Next sentence \\
\end{document}
The first two lines produce the same (incorrect) result. In the first line, LaTeX sees the dot as a non end-of-sentence symbol, so it uses the interword spacing; in the second line, adding \@ to the right of the dot has no effect at all (it would only prevent extra space from being added); the third line will produce the correct result (notice the extra spacing after "WORD.") since by using \@ to the left of the dot, we are telling LaTeX that the dot must be considered as an end-of-sentece symbol.
The fourth and last line produce the same (correct) result, since in the fourth line, LaTeX naturally sees the dot as the end-of-sentence symbol, whereas in the last line the \@ to the left of the dot has no effect at all (it would add extra space which is there already); the fifth line produces a too narrow spacing due to \@ to the right of the dot.
