It is more the type of flower given than the arrangement that provides the symbolism. It's easy to figure out that a cross made of flowers and greenery offers sympathy, or that a cascading bouquet meant for a bride is a symbol of joy. The blanket of flowers donning the winning horse at the Kentucky Derby is congratulatory. Yet the language of individual flowers, perfected by the Victorians, could be flirtatious, utterly romantic or mean-spirited.
In an era where unrelated men and women couldn't be in the same room without a chaperone, there had to be some way to communicate. Sometimes entire relationships were carried out through subtle glances and the exchange of flowers. Red flowers, usually roses, were sent to a lady if the man was totally smitten. Pink roses meant affection, but no commitment. The lady would send a flower back if she was also interested, and one flower only, lest she seem too eager. If either party sent the other a yellow carnation, that meant thanks, but no thanks.
Other flowers delivered messages of another sort. White gilly flowers, sort of like carnations with thicker petals, were often sent to older ladies on their birthday. They symbolized lasting beauty. Purple hyacinths, white poppies and lilies conveyed sadness and condolences. If someone was seen as snooty, he might end up with a sunflower on his porch. Tell a lie, and a snapdragon might be delivered. If someone was considered dim-witted, he might just get a basket of nuts.