Although the Turkish March appears in Beethoven’s incidental music to a play by August von Kotzebue called The Ruins of Athens (1812) its theme had first been used in his Six Variations on an Original Theme (1809).
At the time Turkish music was very much in vogue: indeed, both Haydn and Mozart had also written their own compositions in the Turkish style. Standard to most (including Beethoven’s offering) is the use of the marching pattern “Left … left … left right left …” which is typically also embellished with grace notes to emphasise the characteristic rhythm. Dynamically the piece resembles a passing procession, starting quietly and building to a fortissimo in the middle and then receding back to pianissimo towards the end.
Evidently the music was popular with other eminent composers: Liszt wrote a piano transcription of it in 1846, as did Rubinstein (which was itself later further arranged by Rachmaninoff) and in 1924 Richard Strauss reworked the piece for a new setting.