The word "Renaissance" comes from the French and it means "re-birth." This is an accurate appellation in that everything that encompassed the Renaissance was a re-envisioning of ideas, mores, and artistic expression. Renaissance thinkers embraced learning from classical sources, such as Latin and Greek. They sought to depict realism in the realm of art as well as attending carefully to portraying human emotion. These ideas, although not uniformly adopted across Europe, were widespread.
Let's situate the Renaissance in history before discussing exactly how this period was so new and different. Typically, the Renaissance is thought to begin in the 14th century and ends in the late 17th century. It is book-ended by the Middle Ages (usually dated between the 5th and 14th centuries) and the Modern Era (typically the beginning of the first Industrial Revolution.) The origins of Renaissance thinking began in Italy and then spread throughout Europe.
There were few areas of life that were unaffected by the new ideas of the Renaissance. Here are a few key examples:
Politics: Diplomacy began to gain ground during the Renaissance. Diplomacy meant new negotiations between states through representatives of different nations and even in their own disputes. "Like Byzantine in the previous period, the Italian city-states preferred to use diplomacy as a force in solving disputes among themselves. From Byzantine, the city-states – in particular Venice – also borrowed some diplomatic techniques such as deception, bribery, and espionage. These became the trademark of Renaissance diplomacy."
Science: Observation of the natural world becomes increasingly important. Leonardo da Vinci asked some of the most important questions: "he took the startling approach of actually observing nature and asking deceptively simple scientific questions like, "How do birds fly?" To finish the bill, he then systematically recorded their solutions in his sketches."
Art: "Perceived as a royalty of ancient traditions, [art] took as its foundation Classical Antiquity but transformed that tradition by the absorption of recent developments in the art of Northern Europe and by application of contemporary scientific knowledge." The three (arguably) greatest artists of the Renaissance were Leondardo da Vinci, Michelangelo, and Rafael.