The term "Renaissance man" means sort of an intellectual jack of all trades (and master of all), and in colloquial use it can be just a synonym for polymath stripped of historical context. The root of our expression, though, is the humanist revival mode of education, writing, and thought popular in the--WILD SURPRISE--European Renaissance. The foundational virtues of particularly Renaissance humanism, as opposed to earlier manifestations, was the focus toward civic, public activity and citizenship.

On the face of it, you might expect this would automatically exclude women, on the grounds of both public life and education. In particular, in the late medieval/early modern era, women were systematically denied formal education opportunities outside convents, beguinages that ran schools, and the occasional parish or group primary school. In the later 17th century, as exciting, flamboyant, and brilliant a thinker/writer as Margaret Cavendish was repeatedly denied membership in the Royal Society (she could speak at it, but heavens forbid a woman join), and a grand total of one woman ever received a university doctorate before 1700 (Elena Piscopia, philosophy, University of Padua). And at that point, we are well past what most people would term "Renaissance," especially in its Italian and southern German heartland.

Despite this exclusion, or perhaps because of it, there was a tiny yet thriving tradition of fathers who secured a humanist education for a chosen daughter. As children and adolescents, these "learned ladies" distinguished themselves in Latin and sometimes Greek, poetry and drama, religion and math and philosophy. They were swept up in the trans-European "republic of letters," exchanging correspondence and circulating their original works with the greatest male thinkers of the era. And with very few exceptions, they had to give it all up when they got married.

Lisa Jardine points out that Renaissance "learned ladies" depended on their function as symbols:

From Isabelle d'Este and Thomas More's daughter and the English Tudor princesses, the cultivated gentlewoman is the Beatrice or the Laura of some male humanist's circle, his pupil, his inspiration, his idol.

They served important familial and especially civic functions, too, becoming almost humanist "patron saint" of their city. Nuremberg humanists Willibald Pirckheimer and Christoph Scheurl put a lot of effort into trying to promote Willibald's (incredibly talented) sister, Franciscan abbess Caritas Pirckheimer, as their city's answer to Venice's Cassandra Fedele. When the Holy Roman Emperor made plans to visit Augsburg in 1503, Conrad Peutinger ramrodded into his three year old daughter Juliana a memorized Latin oration to recite, to show off just how intellectual and civilized the city could be. But their civic role could only ever be symbolic. Male humanists like Lauro Quirini, invaluable mentor to Isotta Nogarola, explicitly barred their women students/colleagues from the civic, political, public oriented aspects of humanist engagement and even education (background reading) itself.

And yet--despite their short careers, despite a short-circuited education, despite being understood as curiosities--the learned ladies of the Renaissance managed to accomplish quite a lot in the philosophy, religious, and literary spheres.

To start with one I mentioned above, Caritas Pirckheimer was a cloistered nun! But through her brother, she made epistolary contacts throughout the humanist world, and many of her letters were judged worthy to be printed in Nuremberg in booklets alongside writings by male humanists. While she composed exquisite Latin letters, she also ran her convent and oversaw the composition of its vernacular daybook. During the Reformation, she bravely and forcefully made her community a focal point of women's resistance as Nuremberg turned towards the Luther movement.

Several of the truly "Renaissance" learned ladies took up the mantle of early Italian-French humanist Christine de Pisan, court writer to Charles VI of France at the turn of the 15th century. Venetian Isotta Nogarola (whom Quirini had barred from the study of rhetoric) nevertheless seems to have learned it quite well: she delivered several public orations around the middle of the 15C. She also seems to have developed a personal philosophy of humanism, drawing out Christian patristic authors (in their original language) into contemporary philosophical debates.

Among her early works, Nogarola authored several fairly standard entries in the "querelle des femmes" (long-running academics' argument over women's intellectual and moral qualities, more or less), which drew on the tradition of "eminent women" in history and mythology to defend women's ability to write and philosophize. She also wrote (but likely did not deliver) a sermon against the Turks after the fall of Constantinople in 1453 and various commemorative speeches for funerals and celebrations. But her humanist background, attention to her problematic place as an adult, intellectually-active, unmarried woman in a society where women married young and gave up any public profile, and orientation towards Christianizing humanism then swirled into her most famous work, a dialogue about Adam and Eve (presented as a debate, thus arguing both sides) that took on the question: who was more responsible for the Fall? A popular and polemical question in many hands, in Nogarola's it became a debate on the nature of gender and gender essentialism. Of course, by positing the woman as skilled a debater as the man...

Oh, man, I was going to go on to talk about Laura Cereta's defense of married women against institutionalized domestic violence, and Lucrezia Tornabuoni's nimble use of biblical hero Judith (who beheaded Holofernes)...and then if you want to get away from proto-feminist activity, there's Judith Aylmer (daughter of Lady Jane Grey's tutor!) who was so interested in medicine theory that she learned Greek to read Galen in the original...or Italian Protestant Olympia Fulvia Morata who translated Calvin's works and ended up fleeing invading Catholics for safety, or Marguerite de Navarre...Marguerite de Navarre! Princess of France, Queen of Navarre, fluent in French, Latin, Spanish, Italian and eventually Hebrew, self taught in Greek, organizer of international Protestant intrigue from within a Catholic country, author of a wickedly entertaining series of tales (the Heptameron) more clever but not as dirty as her model Boccaccio, patron of the University of Bourges in her own right (not her husband's)...oh, and the nuns who were incredible artists...ahhhhh...

Of course, Marguerite was a queen, Nogarola chose never to marry (her sister was similarly educated but vanished from the intellectual world when she married at 20), Cereta only enjoyed a public life as a widow, Morata could only watch while her humanist husband received the university positions, Aylmer could only be a scholar and not a practitioner of the medicine she so loved. And without exception, these women were the elite of the elite of the elite, entirely dependent on the goodwill of their family members--not just whoever they could convince to be their patron.

Despite the institutional barriers to participation in the first place, and the restrictions on women's public activity even for the exceptional among the exceptions, some women in Renaissance Europe were awesome enough to earn--or perhaps we should say, were so awesome that they nevertheless earned--the label Renaissance woman.

You might be interested in this recent women's & feminist history thread where the subject of decreasing opportunities for women in the Renaissance was brought up by /u/commiespaceinvader.