LaTeX splits footnotes when it can think of nothing better to do. Typically, when this happens, the footnote mark is at the bottom of the page, and the complete footnote would overfill the page. LaTeX could try to salvage this problem by making the page short of both the footnote and the line with the footnote mark, but its priorities told it that splitting the footnote would be preferable.
As always, the best solution is to change your text so that the problem doesn't occur in the first place. Consider whether the text that bears the footnote could move earlier in the current page, or on to the next page.
If this isn't possible, you might want to change LaTeX's perception
of its priorities: they're controlled by
\interfootnotelinepenalty - the larger it is, the less willing
LaTeX is to split footnotes.
Setting
\interfootnotelinepenalty=10000
inhibits split footnotes altogether, which will cause `Underfull
\vbox' messages unless you also specify \raggedbottom. The
default value of the penalty is 100, which is rather mild.
An alternative technique is to juggle with the actual size of the
pages. \enlargethispage changes the size of the current page by
its argument (for example, you might say
\enlargethispage{\baselineskip} to add a single line to the page,
but you can use any ordinary TeX length such as 15mm or -20pt
as argument). Reducing the size of the current page could force the
offending text to the next page; increasing the size of the page may
allow the footnote to be included in its entirety. It may be
necessary to change the size of more than one page.