Although a whorl can be a spiral in some cases, which makes it sensible to pronounce it as in ‘whirl‘, in botany a whorl is a ring of (three or more) petals, leaves or other parts attached at the same (or very similar) point. I have always, rather uncomfortably, pronounced it as ‘wall‘, probably so I don’t confuse it with whirl – after all a whirl of petals sounds is if the daffodils have been caught in a tornado.
Anyway, whorls of petals, sepals and anthers (in concentric circles) are perfectly normal in most flowers but it is more unusual in leaves, which are usually alternate or in pair up the stems. Whorls of leaves are always very striking and give a special look to the plants, as in the whorls of narrow leaves in veronicastrum (above) and Eupatorium maculatum (below).
While these have many whorls of leaves, trilliums have just one whorl of three leaves, but then the show off with whirls of three sepals and petals.
Many plants in Lamiaceae have whorls of flowers along the stems even though the leaves are opposite, with dense clusters of flowers in rings with gaps between.