These are known as widows and orphans.
These are known as widows and orphans.
> Cobbler's boy and whore's child (in German Schusterjunge und Hurenkind) [1]
I never forgot these two terms.
What you ideally want is every page with the same number of lines, all the lines having the same offsets (grid), each line filled with the same amount of type when you squint, last lines being not too empty and not too full, and no lone first or last lines. Now, when you do your galley proofs and then just cut the paper every n-th line, chances are there will be some orphans and some widows. It follows from geometrical consideration that one of the mentioned constraints then has to be loosened or given up in order to not have orphaned first and last lines. People nowadays scream when you suggest to just leave it that way but really, you have to have some lines with narrower or wider word spacing, or some pages with more or fewer lines, or some paragraphs with a less-than-ideal choice of hyphenation in order to stretch or squeeze the content so it fits in.
As an example, maybe you have just the letters 'me.' on a paragraph last line, which is bad by itself, and that word appears first thing on a new page. That's double bad and easy to fix, maybe just typeset one of the lines above that a little tighter to make the 'me.' find space on the preceding line. Problem fixed, but the price for that is now your last-of-paragraph line is overly full and it is also the last line on the page, which is... double bad, again, like what you started out with. In this case, maybe increasing spacing in the entire paragraph works out better, giving you an orphaned line all by itself on a new page, but at least it contains another word or two.
But that still doesn't invalidate the fact that it is a sign of poor quality.
The offensive naming is a historical thing. I wouldn't call them that today, but can accept the fact that in times not so long gone by this was quite normal. It is like slave/master in IT terms. A historical technical term that should be replaced nowadays.