I’m not going to recreate the wheel. I’m going to quote from Brahms’ entry on Wikipedia and call it good.
Johannes Brahms (7 May 1833 – 3 April 1897) was a German composer, pianist, and conductor of the Romantic period. Born in Hamburg into a Lutheran family, Brahms spent much of his professional life in Vienna, Austria. His reputation and status as a composer are such that he is sometimes grouped with Johann Sebastian Bach and Ludwig van Beethoven as one of the “Three Bs” of music, a comment originally made by the nineteenth-century conductor Hans von Bülow.
Brahms composed for symphony orchestra, chamber ensembles, piano, organ, and voice and chorus. A virtuoso pianist, he premiered many of his own works. He worked with some of the leading performers of his time, including the pianist Clara Schumann and the violinist Joseph Joachim (the three were close friends). Many of his works have become staples of the modern concert repertoire. An uncompromising perfectionist, Brahms destroyed some of his works and left others unpublished.
Brahms has been considered, by his contemporaries and by later writers, as both a traditionalist and an innovator. His music is firmly rooted in the structures and compositional techniques of the Classical masters. While many contemporaries found his music too academic, his contribution and craftsmanship have been admired by subsequent figures as diverse as Arnold Schoenberg and Edward Elgar. The diligent, highly constructed nature of Brahms’s works was a starting point and an inspiration for a generation of composers. Embedded within his meticulous structures, however, are deeply romantic motifs.