Cloning become an important method for conservation genetics. However, it is not a magical solution and doesn't solve all of the the problems. There are two key considerations with conservation: short term issues which are causing the immediate threat such as poaching, habitat destruction etc. and long term issues of genetic variation. Genetic variation is critical to the long term survival of a species because low genetic variation results in inbreeding depression (reduced ability to survive and reproduce resulting from higher expression frequencies of deleterious mutations) and reduced potential for adaptation. The rate of adaptation is determined by the strength of selection and the volume of genetic variation; without genetic variation there can be no adaptive evolution. Therefore, genetic variation is key to the long term success of a species.
Where cloning can come in is it can be used to increase the gene pool, sometimes quite substantially. Consider the meta-population of a species, this could be allowed to include all of the wild sub-populations and all captive or managed (semi-captive) populations. For example, there are ~3900 wild tigers in the world, and ~5000 in captivity. Among all of those, only a subset contribute offspring to the next generation of wild animals, reducing the effective population size, and increase rates of inbreeding and genetic drift. For example, often very few males fertilise the females of a population with strong effects on the effective population size. What cloning could be used for (to various levels, depending on the specifics of the method) is to allow other individuals to contribute. For example, by cloning the members of a wild population that were unable to secure mates during a reproductive season (there is often high variance in mating success which reduces effective population), conservation managers can artificially re-inflate the effective population size to more closely resemble the census population size. In other cases, conservation managers may chose to clone particularly viable/fertile individuals that are approaching old age or nearing death, and are therefore at risk of being lost from the population. Conservation programs could use cloning of (semi-)captive individuals and introducing clones from (semi-)captive populations in to wild populations allowing genetic variation to be drawn from the gene pool of (semi-)captives in to the wild populations. Increasing the variance in the gene pool will increase the adaptive potential of the wild population. Another option is to clone wild animals in threatened areas (e.g. where populations are in decline as a result of poaching) and to put the clones in to safer areas such as national parks, or even zoos, to preserve genetic variation while conservation managers try to bring the other issues under control. Effectively this would act a bit like a seed bank.
However, there are some issues to consider, and this is a non-exhaustive overview. What if there was a good reason for some individuals not mating? The action of selection, which causes adaptation, is to induce variance in reproductive success as a result of the genes an individual carries: in principle selection reduces genetic variation and allows the "better" variants to prosper. So if we clone a wild individual that produced no offspring in the reproductive season we may just be maintaining genes in the population that selection would otherwise be removing. In other words, cloning efforts could be counter-productive to the long-term success of the species and make conservation more difficult. What if we reintroduce bad genetic variance to the wild population? Captive populations have adapted to some degree to the environment that they are in, this may have selected genes out of those populations that are more beneficial in the wild. For an extreme example, dogs are descended from wolves and have adapted to an enormously different environment, so it would probably be very counter-productive to start cloning chihuahuas and introducing them to wild wolf populations as a conservation strategy to get genetic variation from captive "wolf" populations (but maybe the chihuahuas would be a good food source at least). Can clones be effectively, and efficiently, reared and introduced to wild populations? It will be extremely hard to actually get to the point where clones can be successfully introduced to wild populations. Resources (including money), are extremely limited in conservation, so there may be better ways to use those resources. Are populations under remaining threat from short term issues such as poaching and habitat loss? If there is continued extrinsic threat to the wild population then there is not much use in cloning, because clones will also be threatened by the same issues. Many places are still under serious threat from poaching. Adding some clones would be like trying to stop a ship from sinking and using a tiny bucket to bail out the water; you need to plug the hole first or use a really big bucket (can cloning be a big enough bucket?).
Bonus: You could read here about the issues faced in the Isle Royale system of wolves and moose, where wolves are on the verge of extinction, and the impacts it will have on the ecolsystem.