The bacterium E. coli is the workhorse of the molecular biology lab. The biotechnology industry has grown up around using this common bacterium, an intestinal bacterium common to warm blooded animals, to multiply or expand a sequence or segment of DNA for future biotechnological use. The segment usually represents a gene, and we usually refer to this as cloning a gene. The characteristic which makes E. coli such a valuable partner is it's propensity to engulf, consume, or otherwise endocytose, free fragments, or loops of DNA known as plasmids. This property has been further enhanced in proprietary strains of E. coli which are in fact are the only ones that are actually useful in the laboratory. Where as eukaryotic cells, such as mammalian cells, must be transfected using viral vectors or other complex means, a little cesium salt on loop DNA is all laboratory strains of E. coli need to make a meal.
In practice though technicians need to know which cells have transfected a desired plasmid and which cells have not. The common way is to place an antibiotic resistance gene on the plasmid, and put a small amount of antibiotic ( ampicillin ) in the culture media. By doing this, only cells that have taken up plasmids will create colonies will survive.
We are not done. Of those cells which have taken up plasmids, we need to know which cells have plasmids which have our desired insert, or gene that we want to clone. To observe this, we need to make a color marker for each of the colonies that are formed on our plating dish. The reaction that we take advantage of is that if a chemical called X-gal is placed in the culture medium, and the colonies of interest are producing an enzyme called beta - galactosidase, then X-gal is digested into two products, a sugar known as galactose and a blue marker. Thus colonies that are expressing an active beta- galactosidase turn blue.
Researchers have found that beta - galactosidase can be disabled by deleting a portion on either end of the gene. The gene can be rescued by expressing that portion of the gene on a different segment of DNA, or plasmid. The two fragments of the beta - galactosidase gene are then referred to as the alpha fragment and the omega fragment. When they are expressed sucessfully together, it is called alpha - complementation. In practice, one fragment is expressed on the plasmid, and one, complementary fragment, is expressed in the proprietary E. coli cell line that is used. In the ring map of the plasmid shown in reference  , the blue region is the beta - galactosidase fragment. The red region within the blue region is called the multiple cloning site (MCS) or the poly linker site. It consists of a number of sequences that can be cleaved specifically by enzymes called restriction enzymes. These restriction enzymes are derived from bacteria and are commercially available. Their abbreviation indicated the organism they were isolated from, and the number following that is a discovery sequence number. Using restriction enzyme cleavage sites within the MCS, the plasmid is linearized, mixed linear DNA representing the gene we want to clone, and where the ends are complementary ( because of use of appropriate restriction enzymes ) they can be rejoined.
When the cloning vector ( such as pBluescript II ) has taken up a gene, it disables the fragment which complements the beta - galactosidase in the cell, and thus, with no active beta galactosidase, the colonies created are white.
Thus when a technician plates cells, those that have taken up the plasmids without an insert are blue, because the alpha complementation has worked, and those which have taken up plasmids that contain an insert will be white.
The technician or student will then select the white colonies with a pipette tip and drop them into a liquid growth medium, also containing ampicillin. When the desired quantity of E. coli cells have been cultured, they proceed to a mini-prep operation where the cells are liced and the plasmid DNA is separated from other cell contents. This is typically done with a kit containing appropriate solutions and filters. The result being an ampoule of pure plasmid DNA containing the desired gene. This is typically the starting point for modification of the desired gene, or testing of the biochemical properties of the desired gene.
 Stratagene - pBluescript II Phagemid Vectors retrieved from http://www.stratagene.com/manuals/212205.pdf
 Open wetware - beta galactosidase retrieved from http://openwetware.org/wiki/Beta-galactosidase