How specifies that are separated for a river, rocks, mountains, forest ; can at some point not being able to interbreed anymore

Allopatric speciation consists of the geographic separation of a continuous genetic background giving place to two or more new geographically isolated populations. These separations might be due to migration, extinction of geographically intermediate populations, or geological events. In this speciation, some barriers impede genetic interchange, or genetic flow, as the two new populations that are separated can not get together and mate anymore. These barriers might be geographical or ecological.

Vicariance is the geographical separation of an original population into two or more new groups. Discontinuities in the physical environment like rivers, mountains, water, etc., are physical barriers that impede genetic flow between the separated groups.

The process of allopatric speciation involves different steps:

The emergence of the barrier.
Interruption in the genetic interchange
The occurrence of new mutations and their accumulation in time in each population. Slow and gradual differentiation.
Genetic divergence by natural selection and reproductive isolation makes it impossible for the two groups to mate even if the barrier disappears.
Prezigotic isolation mechanisms favored by selection once occurs a secondary contact between the new species in formation.