Widows (the last line of a paragraph at the start of a page) and orphans (the first line of paragraph at the end of a page) interrupt the reader’s flow, and are generally considered “bad form”; (La)TeX takes some precautions to avoid them, but completely automatic prevention is often impossible. If you are typesetting your own text, consider whether you can bring yourself to change the wording slightly so that the page break will fall differently.
The (La)TeX page maker, when forming a page, takes account of variables
\widowpenalty and \clubpenalty (which relates to orphans!).
These penalties are usually set to the moderate value of 150; this
offers mild discouragement of bad breaks. You can increase the values
by saying (for example) \widowpenalty=500; however, vertical
lists (such as pages are made of) typically have rather little
stretchability or shrinkability, so if the page maker has to balance
the effect of stretching the unstretchable and being penalised, the
penalty will seldom win. Therefore, for typical layouts, there are
only two sensible settings for the penalties: finite (150 or 500, it
doesn’t matter which) to allow widows and orphans, and infinite (10000
or greater) to forbid them.
The problem can be avoided by allowing the pagemaker to run pages
short, by using the \raggedbottom directive; however, many
publishers insist on the default \flushbottom; it is seldom
acceptable to introduce stretchability into the vertical list, except
at points (such as section headings) where the document design
explicitly permits it.
Once you’ve exhausted the automatic measures, and have a final draft
you want to “polish”, you should proceed to manual measures. To
get rid of an orphan is simple: precede the paragraph with
\clearpage and the paragraph can’t start in the wrong place.
Getting rid of a widow can be more tricky. Options are
\looseness=-1 immediately after the last word of the
paragraph.
\enlargethispage{\baselineskip} to ‘add a line’ to
the page, which may have the effect of getting the whole paragraph
on one page.
\enlargethispage{-\baselineskip} may produce a
(more-or-less) acceptable “two-line widow”.
\looseness=1 (which should increase the line
length by one) seldom has the right effect — the looser paragraph
typically has a one-word final line, which doesn’t look much better
than the original widow.
This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=widows