Words consisting of two separate words are often separated by an intra word dash, as in x-axis. This dash can be placed between two | characters, for example |-|.
When || is typed, the default intra word dash is used, which is .
The || is also used in word combinations like (intra)word, which is typed as (intra|)|word. The mechanism is not foolproof but it serves most purposes. In case the hyphenation is incorrect you can hyphenate the first word of the composed one by hand: (in\-tra|)|word.
The main reason behind this mechanism is that TeX doesn’t really know how to hyphenate composed words and how to handle subsentences. TeX know a lot about math, but far less about normal texts. Using this command not only serves consistency, but also makes sure that TeX can break compound words at the right places. It also keeps boundary characters at the right place when a breakpoint is inserted.
The table below is an extended version of the table in the "big manual". In the third column, you see what the possible line breaks in the word would be, and the output that would come from that.