Mendelssohn was born in Hamburg in 1809 into a distinguished family and was raised in a particularly cultivated environment. His grandfather, Moses Mendelssohn, had been an eminent philosopher of the Enlightenment and an important literary figure, who fought against the anti-Semitism of eighteenth-century Prussia. Mendelssohn's father, Abraham, was a banker, and he moved with his family from Hamburg to Berlin in 1811 to avoid the terror being waged in Hamburg by Napoleon's occupying forces.

Mendelssohn's prodigious musical talent became apparent at a very young age. He was educated by prominent musicians and his education in general was at the highest level. At the age of thirteen, he was taken to meet Goethe in Weimar. Goethe was immediately impressed with Mendelssohn and over the next nine years they visited each other frequently.

One of Mendelssohn's aunts married the poet Friedrich von Schlegel, and it was his translations of the writings of Shakespeare along with the poetry of Goethe and the works of Jean Paul that most profoundly influenced the Mendelssohn circle. In 1825, inspired in part by Goethe's Faust, the sixteen-year-old Felix composed his String Octet, Op. 20. One year later, Mendelssohn wrote perhaps his most popular work, the overture to Shakespeare's A Midsummer Night's Dream, Op. 21.

In 1825, the medium of the string octet was a novel one. Ludwig Spohr had composed octets that were essentially works for two string quartets in that the instruments were divided into two groups of four. In his Octet, Mendelssohn used the instruments in a variety of combinations and textures. Furthermore, as John Horton has written:

"While the Octet belongs legitimately to the realm of chamber music for solo instruments, Mendelssohn was conscious of its affinity to the string symphony in which he was an experienced practitioner, and had no qualms about implying this in the score: ‘This Octet must be played by all the instruments in the symphonic orchestral style. Pianos and fortes must be strictly observed and more strongly emphasized than is usual in pieces of this character.'"

Mendelssohn dedicated the Octet to the violinist Eduard Rietz, an intimate friend of the Mendelssohn family, who was celebrating his 23rd birthday. The virtuoso demands of the first violin part are striking, and, in fact, one of Mendelssohn's accomplishments in this work, as Friedhelm Krummacher has stated, "was that me made the decisive breakthrough of integrating brilliance with subtlety."

The first movement of the Octet is in sonata form. The slow second movement has a simple, folksong-like theme that undergoes variation. Most popular by far was the third movement, a gossamer scherzo of Mendelssohn's signature type, like the Scherzo from the Incidental Music to A Midsummer Night’s Dream, Op. 61. According to Mendelssohn's sister Fanny, the inspiration for the scherzo in Op. 20 was the Walpurgis Night episode from the first part of Goethe's Faust, specifically the lines: "Floating cloud and trailing mist, Brightening o'er us hover. Air stirs the brake, the rushes shake. And all our pomp is over." The Octet's scherzo was performed at times as a separate piece, and Mendelssohn added wind parts to it, allowing it to be used as a substitute for the minuet movement of his c-minor Symphony. The finale of the Octet is a masterly combination of rondo and fugue, which at one point recalls the opening of the scherzo.