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 page maker, when forming a page, takes account of
\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. This dichotomy 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 have to indulge in 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. If the paragraph is a long
one, it may be possible to set it 'tight': say \looseness=-1
immediately after the last word of the paragraph. If that doesn't
work, try adjusting the page size:
\enlargethispage{} may do the job, and
get the whole paragraph on one page. Reducing the size of the page by
\baselineskip\enlargethispage{-} may produce a
(more-or-less) acceptable "two-line widow". (Note: \baselineskip\looseness=1,
increasing the line length by one, seldom seems to work - the looser
paragraph typically has a one-word final line, which doesn't look much
better than the straight widow.)