Polyploidy is when the number of chromosomes in a cell becomes doubled. This can happen by a mutation that simply makes two copies. It can also happen when the chromosomes from two different species are mixed.
One obvious consequence is that the resulting creature has no one it can breed with. However, this is not necessarily a problem. For example, many plants are both male and female, so they can simply fertilize themselves. Some earthworms can do this too.
An example is the gilia plant from the Mojave desert in California. The species Gilia transmontana turned out to be a hybrid of Gilia minor and Gilia clokeyi. It has as many chromosomes as the other two combined, and its flowers have an intermediate shape. Since chromosomes are not all the same length, we can even say which transmontana chromosomes came from which ancestor.
Even better, we have deliberately re-created wild plants. The first one was the mint Galeopsis tetrahit, which was made artificially by hybridising G. pubescens and G. speciosa. The artificial hybrid was identical to the wild plant and could breed freely with it.
About half of angiosperm (flowering plant) species seem to have originated this way. Relatively few animal species are thought to have originated this way, because not all animals can self-fertilize or reproduce asexually. However, brine shrimp, weevils, bagworm moths and flies seem to have arisen this way.