Flowers worn in the buttonhole of the coat/jacket are referred to simply as 'buttonholes' or boutonnières.
The groom, best man, ushers and usually the fathers of both the bride and groom wear them; sometimes the grandfathers or even godparents wear one too. They are worn on the left-hand lapel of the morning coat or suit jacket.
The buttonholes should not be too large or decorative; something quite simple looks the most effective.
Often, the groom's buttonhole flower matches the bride's flowers.
The best man, ushers' and fathers' buttonholes reflect the bridesmaids' flowers.
Look for a good boutonnière fixing under the left lapel - this small strip holds the flower stalk in place and keeps the buttonhole upright.
The florist should provide some pins for extra support or, if standard suits (i.e. not morning coats) are worn, attaching the flower to the lapel.