|Replica of the star Nelson received as a Knight of the Order of the Crescent. Of the four stars he wore on his coat, this was the one on the right.|
After the Battle of the Nile, Sultan Selim III of the Ottoman Empire (now Turkey, and which Egypt was then part of) wanted to reward Nelson for the victory, by giving him a chivalric honour. However, all the ones in existence at that time in his country could only be given to Muslims, and Nelson was of course Christian. So in August 1799, the Sultan solved the problem by creating the Order of the Crescent especially for him, and Nelson was its first knight. It was later awarded to several other British army and navy officers who achieved success against Napoleon's forces in the Eastern Mediterranean. He also awarded Nelson with the chelengk Nelson wore in his hat.
Perhaps because it had been created especially for him, Nelson was extremely proud of this honour. He wasn't given official permission by the British king to wear it until March 1802, but he used the title after his name after the Battle of Copenhagen in April 1801.
Like all his honours, a replica was sewn onto all of Nelson's coats, but it was upside down! The star was supposed to be to the right of the crescent, but on his Trafalgar coat and the one on his Westminster Abbey waxwork, it can be seen on the left.
Further reading: Ottoman Orders and Decorations