Peri was born in Rome, but studied in Florence. He had several church jobs, playing the organ and singing. He also worked at the court of the Medici family, playing instruments and composing incidental music for plays and madrigals.
In the 1590s, Peri worked for Jacopo Corsi, the most important patron of music in Florence. They felt that art at that time (music, drama, painting etc.) was not as good as the classical art that had been produced 2000 years ago in Ancient Greece and Ancient Rome. They wanted to write drama like the old Greek tragedies. In music they started to write "monody", which meant a solo song with a continuo bass accompaniment. They soon started to realize that just monody on its own could become boring, so they developed it into recitative (where the story could be told) and aria (where the singers could express their feelings in song). Peri and Corsi asked the poet Ottavio Rinuccini to write some words for them and together they produced the opera Dafne. It was probably nothing like what the Ancient Greeks would have done, but it was the first opera in modern times.
In 1600, Rinuccini and Peri wrote another opera together: Euridice. We still have the music Euridice, although unfortunately the music to Dafne has been lost.
Peri wrote several other operas, although they are not great works. However, a very great composer was around at the time. His name was Claudio Monteverdi. In 1607, he started writing operas and his operas are often performed today.
1600 is the date usually thought of as the beginning of the Baroque music period. It is a convenient date because it is when opera started.