Speciation in the process that give rise to new species, also named cladogenesis.

It occurs via splitting of an ancestral species in two or more new ones, or via merging of two old species into a new one (hybridization or allopolyploidy).

Related to the geography of the species, the process can be allopatric (with geographic split), parapatric (with continuous distribution/cline) or sympatric (at same geographic site).

Related to the selective pressures (or lack of it), it can happens via random genetic drift, natural selection (ecological speciation) or sexual selection.

Is hard to generalize about THE necessary condition, because they change depending of the specific biota you interested and to the species concept being used, but I would say intraspecific variability is one that is necessary, but by no means sufficient condition.

Speciation in the process that give rise to new species, also named cladogenesis.

It occurs via splitting of an ancestral species in two or more new ones, or via merging of two old species into a new one (hybridization or allopolyploidy).

Related to the geography of the species, the process can be allopatric (with geographic split), parapatric (with continuous distribution/cline) or sympatric (at same geographic site).

Related to the selective pressures (or lack of it), it can happens via random genetic drift, natural selection (ecological speciation) or sexual selection.

Is hard to generalize about THE necessary condition, because they change depending of the specific biota you interested and to the species concept being used, but I would say intraspecific variability is one that is necessary, but by no means sufficient condition.

It is a wide concept. I recommend to read some books such as following:

1. Ray. F. Evert & Susan E. Eichorn. 2013. Biology of Plants. 8th edition. W. H. Freeman and Company Publishers. pp. 220-229.

2. Mishael G. Simpson. 2006. Plant Systematics. Elsevier Academic Press.

Example:

Homo erectus migrated to Europe but due to selective pressures (climate, diet etc) speciation occured and Neanderthals came to be. Different morphology to that of Homo erectus.

Hope this is a good practical example.

a simple way to define speciation is a lineage-splitting event that produces two or more separate species. 

Examples of speciation by sexual selection/natural selection: More than 500 species of  cichlid fish have evolved in the African great lakes in just a few hundred thousand years

Example of speciation by natural selection: From an ancestral species a ground-dwelling, seed-eating finch,  fourteen species of finches have arisen in the Galapagos Islands: three species of ground-dwelling seed-eaters; three others living on cactuses and eating seeds; one living in trees and eating seeds; and 7 species of tree-dwelling insect-eaters.

One more example: the Galapagos island Daphne Major was occupied by two finch species: the medium ground finch and the cactus finch. Then, in 1981, a hybrid finch arrived on Daphne Major from a neighboring island. It was part ground finch, part cactus finch, and quite large compared to the locals. It also happened to have an extra-wide beak and an unusual song — a mash-up of the songs sung by ground finches in its birthplace and on Daphne Major. The immigrant paired up with a local female ground finch (who also happened to carry some cactus finch genes), and  these birds' descendents were followed for the next 28 years. After four generations, the island experienced a severe drought, which killed many of the finches. The two surviving descendents of the immigrant finch mated with each other, and this appears to have set the stage for speciation because some years afte the drought, the new lineage has been isolated from the local finches: the children and grandchildren of the survivors have only produced offspring with one another.

Hi. Please study speciation books. For example: population, species and evolution of Ernst Mayr. It is very nice book.