Minor genetic changes occurring in a population is called microevolution. They change common characteristics of a species. It cannot explain formation of new species.
Speciation is an evolutionary process of formation of new species.
If a population splits into two such that they cannot reproduce with each other, they are called two species. It can be explained using beetle population.
Consider a huge beetle population spread over a mountain range. Here, each beetle feed mostly on nearby bushes. They do not travel far. So, there will be sub-populations in neighbourhoods.
Most reproduction occurs within these sub-populations.
In rare cases, some beetles might go from one site to another or a crow picks up a beetle from one site to another. As a result, genes of migrant beetle enter new population by reproduction and cause genetic drift (accidental genetic variation in small population).
If a large river comes between two sub-populations, they will be isolated. Thus gene flow between them decreases.
Over generations, genetic drift accumulates many changes in each sub-population. Also, natural selection operates in these different geographic locations. E.g., in one sub-population, crows are eliminated by eagles. Here, the green beetle variation will not be selected. But in other sub-population, number of crows are very high. So green variation will be strongly selected.
Genetic drift & natural selection together makes isolated sub-populations more and more different. Eventually, members of these two groups will be incapable to reproduce with each other even if they happen to meet.
This can be happened by many ways. If the DNA changes are very high (e.g. change in number of chromosomes), the germ cells of the two groups cannot fuse. Or a new variation emerges in which green females will not mate with red males, but only with green males (natural selection for greenness). Thus, new species of beetles are generated.