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This function prints a link to the next set of posts within the current query.
If you need the values for use in PHP, use get_next_posts_link().
Because post queries are usually sorted in reverse chronological order, next_posts_link() usually points to older entries (toward the end of the set) and previous_posts_link() usually points to newer entries (toward the beginning of the set).

Parameter $max_pages is the limit the number of pages on which the link is displayed. The default value “0” means “no limit”.

This function will not work (fail silently) if mysql.trace_mode is enabled in your php.ini. If you can’t edit that file, try adding ini_set( 'mysql.trace_mode', 0 ); to your theme’s functions.php.

See also: previous_posts_link() and next_post_link().