The Rosy Cross is so named in honour of the founder of an occult-cabalistic-theosophic brotherhood (see Kabbalah Cross). He was a German nobleman and former monk named Christian Rosenkreuz (1378-1484). The rose and the cross also happen to be ancient occult phallic symbols; the rose representing female and the cross, male.
Rosenkreuz, whilst travelling through Damascus, was introduced to Asian religious and philosophical thought based on a mystical insight into the Divine Nature. He considered the Church would increase purity much better without the interference of a pope.
God, he postulated, could be experienced better through Nature, rather than through a man elected by cardinals. One of the pope's main jobs in the Middle Ages was struggling to attain, maintain or regain power from various monarchs, which must have left little energy for nurturing Christianity. The door was wide open for antipapists such as Rosenkreuz to flourish.
He, and other brothers of the Fratres Roseae Crucis, applied themselves fervently in the pursuit of understanding the deepest secrets of Nature and to put their knowledge to practical use in helping the sick and needy. Such was the strength of the hidden power of Nature, that the order felt obliged to protect the knowledge by confining it as secret. It was so secret that most of the outside world didn't even know of the order's existence for its first two hundred years.
When the intelligentsia and educated of Europe discovered the fraternity in the 17th century, it must have been an iPod-style revolution with everybody jumping on the bandwagon in search of 'truth'. (This mystical secrecy contrasts with the broader Christian religious thought of not only openness, but a doctrine of actually spreading the Word.)
In the 18th century, Freemasonry connected itself with the occult side of Rosicrucianism and the Rosy Cross was integrated into their symbols. See for example, AMORC www.rosicrucian.org/....