[Take for granted that] mutations occur in living beings. Some of these are neutral (no impact on the organism's ability to survive and reproduce). Others are beneficial (positive impact). And still others will reduce the ability of the organism to survive, thereby reducing its chances of reproducing and spreading the mutation to its offspring. This is called Natural Selection or Survival of the Fittest.
Over time, these beneficial (or neutral) mutations, when passed down and combined with others through interbreeding, will be sufficient to have changed the descendants of any number of one type of organism into a species that is no longer recognizable as the species it evolved from. The specific criteria for a new species is that it can no longer reproduce with members of the original species.