Fasciation (AKA cresting) is a mutation or disease that appears on rare occasion in vascular plants; specifically, the growing tip, instead of forming a point, forms a line. This means that stems grow to look like flat ribbons, flowers grow in long ovals, trees grow a tangle of branches, and cacti form fleshy fans. This mutation may also cause increased growth in the affected part of the plant. While fasciation is most commonly recognized as affecting the heads of flowers, it can also occur in branches, stems, roots, and fruits.
Fasciation is valued in some plants, particularly flowers and cacti. In most cases the widening of the growing tip is only 2-6 inches, although in the some plants, such as the fasciated cristate cactus, it may be several feet wide. The wide blooms and fans resulting from this can be quite striking -- and in some cases, freaky-looking. Unfortunately, there is no reliable way of causing fasciation in most plants, although in woody plants it can be propagated through grafting and in cacti it can be cloned through vegetative propagation.
Ironically, despite being quite rare, fasciation can be caused by any number of factors, including genetic mutation, hormonal imbalances, and bacterial, viral, or fungal infections. Risk factors include exposure to herbicides, insects, damage to the growing tip (including frost damage), and any factors that cause accelerated growth. Fasciation can be bred in some plants, and was in fact one of the seven traits that Gregor Mendel used to illustrate the concepts of dominant and recessive traits.
The most well-known fasciation-bearing species (among botanists) is the cockscomb celosia, although there are other species that have reliable (or semi-reliable) fasciated cultivars. These cultivars are commonly given Latin cultivar names of Monstrosa, Cristata, or Tortulosa (monstrous, crested, and twisted). The word 'fasciation' comes from the Latin word fascia, meaning 'a band', referring to the stem's resemblance to a wide band or ribbon.
References and further reading:
The Wisconsin Master Gardener Program: Fascinating Faciation (Good photos here).
Fasciation: Fasciating distortions of the plant world, Curtis E. Smith