Floret: One of the individual small flowers of a clustered inflorescence, e.g. sunflower.*
Coneflowers, Echinacea purpurea, are in the Asteraceae (sunflower/daisy family). Like all members of that family, their ‘flowers’ are actually made up of many closely packed florets. Each petal around the edge comes from a separate floret, called a ray floret. The ones in the centre which produce the seeds are called disc florets.
*Allaby, M. (2006). A dictionary of plant sciences (Revised ed.). Oxford: Oxford University Press.