Simply put, genetic drift is the change in allelic frequencies due to chance. This phenomenon is particularly important in small populations as a smaller population size increases the importance of chance effects.
An general illustration of the principle will certainly elucidate this principle. Suppose there is a population of organisms, and in this population, a new allele arises with good potential of having a profound effect on the allelic frequencies in this population. But, some catastrophic event happens (a flood, a fire, a disease, …) and all the organisms carrying the new allele are wiped out. If this is the case, the allele frequencies of that population will look different than when natural selection was allowed to run its course.
Vice versa, a new allele can spread quickly if most of the organisms are pushed into extinction, aznd the few that remain just happen to have a certain allele. This allele will thus have a much higher frequency then before the catastrophic event.
These examples of course are oversimplifications, but nevertheless, they illustrate that chance can have a profound effect on the allelic frequencies in a population.