Genetic drift is more likely to occur in small populations because when a mutation arises in a member of such a population, they, and potentially their offspring, constitute a much larger proportion of the population than a mutated individual would be in a larger population. As their offspring interbreed with others, the new trait is much more likely to become widespread. A larger population would tend to drown out mutations.
Genetic drift is an entirely random process without any need for natural selection. It is the tendency of isolated populations to change genetically in random ways over time. Because genetic drift does not rely on natural selection to spread through a population, it can easily bring on negative changes. In isolated populations, the lack of competition can allow such disadvantaged populations to survive, where in a larger population they would be out-competed by their more fit neighbors without the mutation.
Because diploid animals such as humans have paired chromosomes, any mutation will only happen in one. If it is a dominant mutation, it will have an effect on the organism, but if it is recessive, it will not. This can allow lethal mutations to spread through a population, because neither the original organism nor its offspring will manifest a change. Such mutations can only show themselves if two individuals with one copy of the gene breed, in which case there is a 25 percent chance that they will have two copies of the mutant gene.