I think organic traffic means traffic that comes naturally more likely from SEOs backlinks, trackbaks. Not traffic from banner ads, google ads, anything that involves money. Thats what I think.
Organic traffic is traffic generated naturally from people searching in a search engine and stumbling upon your domain, Organic traffic is invaluable because it costs nothing so any revenue from that type of traffic is 100% profit. For example I have Proxy A name gomimmy.com and Proxy B names Unfilter.Us now no one I know of would type in gomimmy to find a proxy so Proxy A relies on referallys to get traffic while Proxy B gets a ton of organic traffic from people typeing unfilter into search engines.
Web traffic which comes from unpaid listing at search engines or directories. Organic traffic can be generated or increased by including the web site in directories, search engines, guides and award sites.