The "black hat" term means something that is bad, unlegitimate etc. White hat on the opposite is something legitimate and trusted. Speaking of SEO, the black hat SEO is using methods that are prohibited by Google or violate its guidelines. Normally, you should avoid black hat methods, but in the real world there is no pure white hat SEO. All methods are "grey", some more, others less.
Blackhat seo is such techniques in SEO in which content & links are aimed at search engines.All those methods are looks like spammers.In blackhat SEO search engines works as their enemy.Black hat sees domains or branding as inconsequential. and Whitehat seo is such techniques in SEO in which content & links are aimed at human.All those methods looks like a healthy Naturally Occurring Backlinks and healthy discussion.White hat sees search engines as their ally.White hat sees them as something to be nurtured.
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To explain it in simplest form and that everybody will understand. Black hat is like a illegal activity of optimizing a website while white hat is the legal way of optimization.
The natural way to increase the ranking of your web page is named as the White Hat SEO, the un natural way to increase the ranking is the Black Hat SEO.
Blackhat is or may be considered by most people as illegal or imoral tactics to force your site to the top of SERPs where as white hat is legit tactics such as commenting on blogs, forums, proper link building, etc.