This principle is applicable to all living cells - not only orchids.

Basically, each cell has the capacity to multiply. The process of multiplication is called cell division. In lower organisms like bacteria and some fungi, the process is extremely simple and corresponds roughly with 1 of the methods in us humans. Mitosis and Meosis are the two methods of cell division in humans as well as in plants including orchids. While mitosis occurs in all cells of the body for maintaining the growth,etc., Meosis or reductional division occurs only in specialized GERM CELLS which are concerned with reproduction - by producing specialized cells called gametes. During fertilization, these gametes fuse to form a ZYGOTE which is a single cell from which the entire organism grows.

The 'n' used in all these descriptions refers to basically a "HAPLOID" number - that is the basic number of set of chromosomes. Chromosomes are nothing but the genetic material in the form of DNA complexed with a large set of proteins. It is visible only during a particular phase of cell division after treatment with static drugs including colchicine and many more. In humans and mostly almost all other living organisms, the normal number of chromosome sets is a DIPLOID number or 2n. Any variation from these usual normal number of sets is called ANEUPLOIDY and includes TRIPLOIDY, POLYPLOIDY, etc.

In plants, however, due to various reasons - both natural as well as human induced, these number of chromosome sets in the individual cells is as high as 16n. The genetic material or DNA - collectively called the "GENOTYPE" codes for numerous proteins, enzymes and other components that together interact, are complexed together to give the final physical form or the "PHENOTYPE" of that organism. So in cases of plants, the more the number of copies of the genes, the greater they're expressed thus greater protein build-up and thus you get better varieties. This is the basic idea behind Bio-engineering of genetically altered vegetables and stuff. In case of orchids, I presume (have not read any specific data or information - but based on what I understand), that as the number of chromosome sets is increased in aneuploid varieties like 3n, 4n, 8n, etc., the net protein expression is also increased - thus you get better looking flowers, better quality and the sort. However, this is not necessarily true always because a lot of times, these aneuploids are not viable or capable of surviving and rather than being more better varieties actually turn out the exact opposite.

Hope this is helpful.