Nonbreaking spaces are HTML space characters - expressed as 'ampersand-n-b-s-p-semicolon' ( )- which browsers treat as a non-space when deciding where to break lines of text.

For example, if you want to keep the words 'Pig and Whistle' as a single, non-broken chunk of text

(unlike, say, 'Pig and
Whistle', assuming that
in this instance the
text is in a narrow
column and that there
is a line break after
'and')

one would insert nonbreaking spaces between the words 'Pig' and 'and' and 'and' and 'Whistle'.