Pay-per click advertising allows you to buy key words and have them linked to an advert. Just like an auction you are pitted against your competition in a bidding war where whoever bids the most is given a spot on their page. There is no guarantee where or when you will be positioned on their page.
Just as the name suggests, when people click on your pay-per-click advert it costs you money. There are no limits to the number of key words you can register but the downside is you can pay up to $15 for every click, and 98% of those people will just be browsing. This can be very expensive with a budget of at least $10,000 needed (and sometimes much more) to run an effective campaign.
Organic links are the natural search results presented by a search engine when someome does a search. These are links money can not buy, however, using a few clever techniques all search engines can be manipulated. Being present in the first few organic links is the holy grail of online marketing because people trust organic links more than pay per click ads.
Organic search positions are highly contested and there is a lot of work that goes into securing them. It is acheivable but in most cases you will need the guidance of a professional. This is a more cost effective solution with an average spend of under $5000 required.
Unlike pay-per-click advertising there are no fees due when people click the organic links.