The English Renaissance began in the late fifteenth century but is primarily identified with the sixteenth and early seventeenth centuries, the period of Henry VIII, Elizabeth I, and William Shakespeare.
Because large numbers of classical texts and ideas were being translated into English during this period (helped very much by the rise of the printing press), new words entered the language in droves. Some words were simply imported "as is" from other languages, while some were invented to describe concepts that had no word yet in English. (Today's world is in a similar shift due to the rise of the internet and related computer technologies: a flood of words from webinar to texting have entered the language, which simply did not exist twenty years ago because what they describe did not then exist.)
Because of the new focus on the classical world, many Latin and Greek words were brought into the language and simply "became" English, such as mythology, chaos, skeleton, and anatomy. These words reflected the intense interest in subjects such as science and Greek myth.
Shakespeare is famous for inventing hybridized words to fill gaps in the language, such as "barefoot," but other writers, such as Ben Jonson, did so as well. Other words, such as the Latinate "dexterity" and "ingenious," were coined by writers and scholars who wanted to emphasize their prestige by their links to classical learning.
As mentioned before, the printing press helped to standardize the language, uniting various dialects and rapidly introducing new words. Periods of foment and change tend to alter languages, and by the end of the English Renaissance, the groundwork for Modern English (usually identified as starting around 1700) were laid.