Memetics is a sub-discipline of evolutionary science, like genetics.
There are also sub-disciplines within memetics.
As genetics has multiple applications
(genetic sequencing, chemical paleo-anthropology, genetic screening & counseling, etc),
so does memetics.
Genetics is the study of the first identified replicator, the DNA molecule and component genes.
Memetics is the study of the second identified replicator, the memeplex and component memes.
Memes are bits of information transmitted from mind to mind. Some memes and groups of memes (memeplexes) are structured in ways that encourage brains to copy them more than others. They integrate with biological drives and human emotions, ensuring viability. These memes are the foundations of human cultures which spread through populations and over generations.
When people talk about memetics, they tend to begin with human culture and language. Memes have been viewed as unique to the human species, originating from our massive brains & aiding survival of an otherwise hairless and defenseless ape.
The phenomena of human cultures are, as far as well can tell, unique in the biosphere. However, the beginnings of memes (protomemes) are quite common. Chemical signals network bacteria, hyphae and the social insects. Visual displays and postures communicate fitness, attract mates and deter predators in vertebrates and cephalopods. Vocalizations relating to threats, food, mating and care of the young are observed in rats, whales, and wild turkeys. These chemical signals, visual displays and vocalizations are ways for individuals to send information over distances, rewarding the participants with survival advantage (and often pleasure as well).
These forms of networking provide the scaffold for cultural memes to develop. They also select for the internal biological systems in each human individual which allow them to interface with memeplexes. Humans have been playing with memeplex development and design since prehistory when we painted the caves of Lascaux, buried our dead in beads and flower garlands and told stories about the stars. For countless generations we relied on our own minds and those of others to store the data and skills necessary for survival. We encoded the most vital parts of our survival strategy in ritual and taboo, so that the very old and the very young could retain information and spread it to others, ensuring true transmission even with the unreliable hardware that is the human mind. We did this without being wholly conscious of it.
Ritual and taboo were memory aids, improving the storage and transmission of extragenetic information. Our clothing, our tools and our rock art functioned as memory aids. They stored data which could be deciphered with careful attention and study even without personal knowledge and experience. However the greatest information could only be obtained through an item's ability to interface with information already stored within an individual mind. This was the beginning of extrasomatic data storage.
With the development of writing, more data could be stored outside our bodies. Carving stone and clay gave us the perception that words endure forever. We became enchanted with the power of written language. Numbers and history became important. We became less aware of how text, like artifacts, do not simply impart new information to a reader but instead are perceived through the lens of previously acquired information. We began to dream of permanence and this illusion built upon itself.
We altered our environments and developed symbiotic relationships with domesticated species. We also domesticated ourselves. Memeplexes provided food, clothing and shelter as well as companionship. They enabled us to settle in large cities and maintain them. We were able to accomplish more together than we ever could alone. There were trade-offs. There always are.
We weathered the agricultural and industrial revolutions. We transitioned from feudalism to capitalism. We co-evolved with religions, helped them spread, interbreed and compete for minds and resources. Different political systems evolved to meet the environmental demands of particular regions and then struggled and cooperated to survive.
Cultural evolution was (unfortunately or fortunately) an idea born before its time. It arose within the context of European Imperialism and Malthusian fears of overpopulation. It came endowed with an inheritance of political revolutions, Enlightenment ideals and Christian revivals. Evolution equaled development and progress. "Primitive" meant something less, something "sub". It was an intuitive leap to say cultures, technologies, religions and such "evolve", but it was one which the educated could easily accommodate. Such ideas evolved into the conglomerate labled "Social Darwinism" (erroneously named as Darwin did not originate this idea) based on now-dead and decaying branches in biology, and diverse hypotheses in criminology, sociology and scientific racism.
Darwinian evolution had the previous genetic work of Mendel and the taxonomy of Linnaeus. It weathered the ensuing storm and was able to dispel its associations with debunked pseudoscientific hypotheses. It became the foundation for modern evolutionary science (which has greatly exceeded the limited perception of Darwin).
However, the social sciences (especially Anthropology) found the idea of Cultural Evolution to be inextricably tied to the concepts of Social Darwinism, Scientific Racism and the like. Lacking the idea of a replicator, Cultural Evolution was left open to breed with a certain strain of Christian morality and European economics, creating a particularly nasty hybrid with the stamp of "rational", "scientific" and "progressive". There was backlash. A new social consciousness, based in a competitive branch of Christian morality and economic ideals, highlighting the equality and brotherhood of all mankind was taking hold. The first incarnation of Cultural Evolution proved too inhumane and too dogmatic to withstand the gentler inclinations of human nature.
The idea of a second replicator, a meme, is incredibly powerful because it gives us enough distance to analyze cultural phenomenon independent of specific human actors and aside from our cultural bias and moral judgments. It can no longer be used to justify the call of "Exterminate, Exterminate!" (though some atheists would certainly try). It asks us to dig deeper and comprehend how complex ideas have evolved to motivate collective human actions.
We can step away from the initial revulsion when faced with unpleasant cultural phenomena such as Nazi book burning or Aztec human sacrifice and instead investigate how such practices emerged and were conserved within a human population.
Memetic theory is a thought tool. Like any tool it can be utilized for peace or sectarianism. Please do not overlook Memetic theory because you cannot relate to some who have supported it. Memetics is no more a tool for vociferous atheists than it is for ardent adherents of one religious tradition or another (though as with any good tool, many may try to appropriate it for themselves alone).
Memetics allows us to further comprehend how complex social phenomenon develop from the same selective environmental pressures which shape biological evolution. That is all. It is up to each of us to struggle with how we will integrate this knowledge with our beliefs and values.