When each of the many (more than 2) flower pedicelsarises from around the same point at the tip of its peduncle, it is termed umbel arrangement. This arrangement is often compared to that of the struts (ribs/frame) of an umbrella.
Many of the species in genera Bulbophyllum are examples of this unique characteristic. Flowers in umbels are referred to as umbellate, or occasionally subumbellate (when flowers are almost umbellate).
Resupination in orchid flowers is the process by which the pedicel twists to position the lip at the bottom side of the flower. Orchid flowers have one of its petals modified as “lip”, usually the top one. As the bud develops, its pedicel makes a 180° twist to arrange the lip at the bottom side. It has proven that this twist happens to position the lip in such a way to make itself a landing pad for visiting pollinators.
Those flowers with lip at the bottom are called resupinate flowers and those at the top are called non-resupinate flowers (or not resupinate). Majority of the orchids have resupinate flowers.
It may be tricky to understand, hence, I am making it simple here. Look at the 2 pics carefully, flowers with the apex of the lip pointing downward are called resupinate flowers and the other, pointing upward are called non-resupinate flowers.