It is generally believed that Bach’s Six Suites for solo cello were composed between 1720-21, shortly after the completion of the sonatas and partitas for unaccompanied violin (see Classical Music with Alto, Volume 1 for the Allemande from Partita no. 2 in D minor from that set). At that time (1717-23), Bach was Kapellmeister at Cothen. Kapellmeister was an entirely secular position, so Bach was not required to compose religious music but needed to write pieces such as sonatas, partitas, orchestral overtures, or suites to satisfy his patron. 

 

It is possible that his good friend Christian Ferdinand Abel (a viola da gamba player and cellist in the court orchestra) was the first to play his cello suites. The technical demands of the suites suggest they were written for a highly skilled player.

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Bach is quite possibly the first pioneer who composed pieces for solo cello. Before the middle of the 18th century, music written specifically for solo cello or containing obbligato cello parts were very rare. In Austria and Germany, the cello appears to have been used primarily as a part of the continuo group to strengthen the basses.