The phrase "genomic imprinting" has come to refer the turning off of a gene (a particular instance of a gene on a particular chromosome duplicated across the cells in a body) so that the gene is not expressed at all, with the turning off of the gene not caused in the body in question, but rather, during the previous generation by a process happening in the soma of one of the parents. A maternally imprinted gene is passed on to junior, but will not be expressed in junior. a paternally imprinted gene is passed on to junior, but will not be expressed in junior. Typically (as far as we know) a gene is imprinted by neither parent, one parent (as in always the mother) or the other parent (as in always the father), but never both parents.
There is a little oversimplification going on here, but not much. "Imprinting" can happen through more than one mechanism, and as far as I know, at least one of these mechanisms has other functions and probably evolved early in the history of life for reasons that have nothing to do with paternal imprinting.
(I quickly add that since we don't really know the exact mechanism for imprinting in mammals, we can't rule out the possibility that a maternally imprinted gene is sometimes, even often imprinted by the male parent, and visa versa. But it is probably also true that having both genes imprinted is very problematic so these instances would either be well known rare disorders or, more likely, early aborted reproductive events. There is a handful of such disorders known and they are thought to related to incorrect chromosomal arrangements, not cross-sex imprinting.)
Although imprinting has been looked at a number of times and there are a few different models to explain its evolution, the most recent, well developed, and interesting explanations are those proposed by David Haig. Haig notes that imprinting is complementary with respect to a particular trait such that if an individual receives two imprinted genes or two non-imprinted genes (which would normally be impossible) for a trait in which imprinting happens, the associated phenotype is extreme. He then notes that the outcome of this trait would resemble (if the individual could survive with it) an extreme parental strategy suited to one, but not the other parent.
The classic example would be a trait that grew placental tissue. The placenta is an organ of the offspring. It is the first organ that you lose during your lifetime (later you'll lose wisdom teeth, maybe an appendix, and if you buy a house, an arm and a leg, etc.). The job of the placenta is to extract energy from mom. From dad's point of view, in mammals (which are internally fertilized) a good strategy might be to extract ALL of the energy from mom. Grow the baby big, fast, and strong, suck mom dry in the process, and it really does not matter if she can reproduce again. Dad has no real guarantee that the next baby to be nourished by this particular female is going to be his anyway.
From mom's point of view, it is better to allow the offspring in utero to have just the right amount of nutrition via the placenta, so she can continue to invest (perhaps) in previously born offspring, and/or prepare for future offspring.
If there are genes that regulate the relative distribution of energy towards growth of the embryo exclusive of the placenta, vs. the placenta itself, then one might expect the pro-placental genes and the pro-embryo genes to "line up" with a parental unit, and/or the facility to turn on or off a gene by one parent to be offset by the other parent. And that is in fact what happens.
I'm skipping over lots of details here, but let's just say that in mammals there seems to be genes turned off by dad vs. mom that, if either is reversed in its effect, the result can be as extreme as either all-placenta or all-embryo (neither of which is viable). There are a couple of in between conditions that probably involve a smaller number of genes being affected. Also, the extreme and non-viable versions of this sort of thing can be observed in mice by producing all-or-none fertilized eggs and combining them with normal eggs early in development to produce a chimera that is affected but viable.
So, in short, Haig's theory is that imprinting evolves in the context of parent-offspring conflict (in relation to conflict among parents or potential parents).
The paper at hand, by Edwards et al., looks at the evolution of imprinting across mammals. Imprinting may be unique to mammals, but within mammals, is there a pattern?
From the author's summary:
...Here we have shown that all the genes in one genomic region, Dlk1-Dio3, which are imprinted in placental mammals such as mouse and human, are not imprinted in marsupial (wallaby) or monotreme (platypus) mammals. This is in contrast to a small number of other imprinted genes that are imprinted in marsupials and other therian mammals and indicates that imprinting arose at each genomic domain at different stages of mammalian evolution.
The genes in this region are generally associated with the placenta.
I would argue that this supports Haig's hypothesis. The non-placental mammals may have a different calculus for parental investment, and there are important mechanistic differences as well. With early separation (via an egg or an altricial offspring) females have enough additional control over offspring strategies for garnering nutrition from the mother that there are few paternal strategies involving maternal nutritive supply that can be exploited, and thus, a maternal counter strategy using imprinting need not evolve.
Edwards, C.A., Mungall, A.J., Matthews, L., Ryder, E., Gray, D.J., Pask, A.J., Shaw, G., Graves, J.A., Rogers, J., Dunham, I., Renfree, M.B., Ferguson-Smith, A.C., Ponting, C.P. (2008). The Evolution of the DLK1-DIO3 Imprinted Domain in Mammals. PLoS Biology, 6(6), e135. DOI: 10.1371/journal.pbio.0060135
Of course if we were really as monogomous as we claim, there would be no imperative for imprinted genes of this sort in humans. Family values and all that.