The term Rosicrucianism came into use as a result of 2 anonymously published manifestos, the Fama Fraternitatis and the Confessio Fraternitatis in 1614 or thereabouts. The texts were published in German and Latin. The Chymical Wedding of Christian Rosenkreutz followed later.
The Fama relates the history of the mythical Christian Rosenkreutz, a German who goes to Damascus to study the wisdom of the Arab sages in the 13th century. Upon his return, Rosenkreutz recruits 7 brothers to found his hidden order. The Fama relates that the tomb of Rosenkreutz was opened 120 years to the day after being sealed, which was predicted by texts found in the tomb. Generally, the Fama and subsequent documents speak of an order of hidden masters that has decided to make itself known while remaining anonymous. The manifestos invite people to seek and vaguely promise a possibility of admission to the Rosicrucian circle to those found worthy.
There exist many organizations which call themselves Rosicrusian, such as the AMORC (Ancient Mystical Order of the Rosy Cross) but there is no demonstrable continuity of tradition between these and the enigmatic authors of the manifestos.
The Cassiopaean material makes multiple references to Rosicrucians. According to that source, there is an ancient hidden fraternity that is behind the manifestos but is vastly more ancient, having its source in a pact between humans and fourth density service to self beings. Organizations such as the Illuminati and the inner circles of various secret societies are offshoots of this.