So sang Bing Crosby. In the current context, however, it describes the chopping of a word into two halves, each half with the same number of letters. Hence only words with an even number of letters can be considered. The letters of the first half and second half, respectively, of a parent word are rearranged to make two new words, the offspring.
"Straight Down the Middle,"
Word Ways: Vol. 37
, Article 17.
Available at: http://digitalcommons.butler.edu/wordways/vol37/iss2/17