The liger is an example of how our definition of what is a species is our best effort, but it doesn't always work. Many times, you can have two organisms that are VERY closely related, enough that there can be some breeding between them, but in general we consider them different species. A tiger and a lion are like that. In the wild, they never encounter each other (they live in very different parts of the world), and if they did, they'd likely attack each other. It's only in zoos, etc where they meet and occasionally in those weird circumstances where they wind up mating. I don't know much about the evolutionary history of the big cats, but I wouldn't be surprised if tigers and lions share a fairly recent common ancestor (fairly recent being maybe 1 million - 200,000 years or so). I did a quick google search and the site below says the rare natural hybrids are usually sterile