When we talk about organic search engine traffic, we're usually just talking about the free traffic from search engines, as opposed to the pay per click search engine traffic. Quite often people confuse organic search engine optimization with safe "white hat" SEO.
Organic just means that it's referring to the organic search engine results – i.e. the free results not sponsored listings. I think it's very important that people make this distinction, as I believe a number of people are more focused in organic search engine optimization services, assuming that organic is as safe as white hat SEO.
Image Source: Google
If you were looking for safe SEO, then what you're looking for is white hat organic SEO – because the word "organic" is mentioned it doesn't mean to say that its safe white hat organic SEO.
The difference between Safe White hat organic SEO – and the alternative:
The difference is that safe, white hat SEO is based on good common sense SEO, to give the search engines what they want – the alternative, is tactics which attempt to trick the search engines into thinking we're giving them what they want (good, relevant & valuable content) by using risky shortcuts & loopholes.
There is really no secret to good effective & safe SEO, you start with good keyword research, making sure you're going after the right keywords (the most important part of SEO in my opinion) you decide on a way forward depending on the market & the required results.