How does variation lead to evolution?

Hint: Variation, in genetics, in any distinction between cells, individual individuals or groups of organisms of any type, owing either to genetic variations (genotypic variation) or to the influence of environmental influences on genetic potential expression (phenotypic variation). Physical appearance, metabolism, fertility, mode of reproduction, behaviour, learning and mental capacity, and other visible or observable characters can display variation.

Complete answer:
-Changes in the number or arrangement of chromosomes, or differences in the genes borne by chromosomes, are responsible for genotypic variants. Genotypic differences are skin colour, body shape, and disease tolerance. Individuals with several chromosome sets are referred to as polyploids; many typical plants have two or three times the average number of chromosomes, and this form of variation can result in new species.
-By examination of the host, a mutation will not be defined as genotypic; breeding tests must be conducted under regulated environmental conditions to establish if the change is inheritable or not.
Variations produced by the atmosphere may arise from one factor or the combined effects of many factors such as temperature, food supply, and other organisms' behaviour. Phenotypic differences also include phases in the life cycle of an organism and seasonal variations in an individual. These changes do not require any genetic modification and are not passed to subsequent generations in general; they are thus not essential in the evolutionary process.
-Variations are categorised as either constant or quantitative, or as qualitative or discontinuous. A discontinuous variation is known as a polymorphic variation, with many classes, none of which is very small. Examples of polymorphic diversity include the division of most higher organisms into males and females and the appearance of multiple types of butterfly of the same genus, each coloured to blend with a particular foliage.

Note: The differences expected to make improvements have never been empirically identified from one species to another species. These modifications are more properly interpreted as Darwinian evolution or macro evolution. In evolution or transformation, differences are the driving force. Only current variants will function upon natural selection. So there must be differences in order for evolution of some sort to happen.