Sometimes a group from a population are separated from the main group geographically. Due to the lose of certain genes on both sides, new species emerge over generations. This is called allopatric speciation. Happens most often with small and isolated populations.
A new species can also arise from the same geographic area as the parent species. This is called sympatric speciation. This occurs when mating. Some of the resulting gene flow is reduced by different factors. Many plant species have evolved from this accident during cell division, where an extra pair of chromosomes is present. These are called polyploid, meaning they have two complete sets of chromosomes.
The evolution of many species with a common ancestor is called adaptive radiation. The adaptations they undergo better suit their environments and their rolls in that community.
Speciation can occur rapidly or slowly. Stephen Jay Gould and Niles Eldridge are both paelientologists. Together they created the term punctuated equilibria. This describes the long periods in which little change among a species happens, punctuated by abrupt episodes of speciation.