A snicker is a disrespectful snort of half-suppressed laughter, often expressing superiority. We snicker at beauty queens talking about world peace, for example.
Used indiscriminately with the word snigger, though snigger tends to have a more specifically sexual tone. As in, "I couldn't help but snicker when the Customs Officer said: 'Next time please declare your nuts.'" Try saying that without sniggering or snickering.
