How are variations passed down through generations? What makes this possible?

Variations are any differences in traits in a population. For example, humans vary in height, giraffes have different length necks and some snow geese are white while others are gray or 'blue' in color. A variation will get passed on to the next generation when an individual reproduces. Some variations will provide an advantage in reproduction so those variations will get passed on more often. Over generations, certain variations will become more common in the population. This is how populations change through evolution by natural selection. 

One of my favorite examples is lactase persistence in humans. Lactase is the enzyme that breaks down lactose (the sugar in milk) so that it can be digested and used by the body. In almost every mammal, the lactase enzyme stops being produced after infancy. However, worldwide 35% of adult humans can digest lactose. They continue to produce the lactase enzyme throughout their lifetime. This is an example of variation in the population because some people can digest lactose and some people can't.

When scientists have studied the genetics of lactase persistence, it turns out that it is caused by a single point mutation in DNA. A few different groups have different mutations that allow for lactase persistence, namely groups in Northern Europe, West Africa, and the Middle East. In each of these populations, early groups of humans kept domesticated cattle and used dairy for food. In times of drought or famine, milk proved to be a non-contaminated food source packed with nutrients. People who could digest milk had an advantage in survival. These people survived and then reproduced, passing on the mutation that allowed for lactase persistence. Over generations this variation became more common in those populations. 

In summary, variations are passed to offspring through reproduction, and when certain variations provide a reproductive advantage they will be passed on more often by the individuals that survive to reproduce. This is how evolution by natural selection works.