traditional refers to the standard writing system of chinese culture, which has evolved over the last 2500 years. (note - in chinese language, this is usually referred to as 繁體字, literally "many" or "complex" script - as compared to 簡體字, literally "simple script"). in some chinese societies (typically those not in Peoples Republic of China), traditional chinese can also be called 正體字 which literally means "formal" or "correct" script.
the simplified script standard evolved from writing 'shorthand' chinese. the communist chinese government (people's republic of china) created and standardized the "simplified script", drawing from convention as well as further simplifying characters. there is a history of this on wikipedia which can go much more into detail.
when you see "traditional chinese" it refers to the chinese writing system which has existed since 2000-3000 years ago, and is still in use in places like Taiwan (Republic of China), Macau, Hong Kong, and overseas chinese communities in the west. it is known as "traditional" because it's contrasted with the system which the PRC government (the communist chinese government in mainland China) established about 50 years back, which has not replaced the traditional writing system as the main system of writing in other cultures not ruled by that government.
something the other answers have not noted, which you may not realize, is that many characters in the "simplified system" are the same as in the "traditional system" (i'd say somewhere around 30-50% are the same in each, examples: 人,一, 二,你,好, and many many more). the “繁” character, which means complex in "繁體字“( traditional or complex script), looks pretty complicated right? well, it's the same in simplified chinese! so really, the only way to know this is to have learned, or to consult a dictionary.