Yes, ligers are the offspring of a male lion and female tiger. The offspring of a male tiger and female lion is called a tigon. Ligers tend towards gigantism and are generally larger than either of their parents, whilst tigons are generally smaller or at least no larger than their parents. Like most hybrids, both are usually sterile, but occasionally a female will be fertile and can be bred back to a male lion or tiger, producing:
Lion + liger = li-liger
Lion + tigon = li-tigon
Tiger + liger = ti-liger
Tiger + tigon = ti-tigon
There is no record of fertile males, so you could never breed two ligers or two tigons together, or a liger with a tigon.
Respectable zoos frown on the breeding of hybrids such as ligers and tigons, as they have no value from a conservation point of view and are taking up space and resources that could be used to breed endangered species. They are basically freaks bred by unscrupulous zoos in order to make money out of people willing to pay to see them.
Today, there is very little chance of them occurring in the wild – tigers are found only in Asia, lions in Africa and the Gir Forest of India, where there are no tigers. Historically, the Asiatic subspecies of lion had a much greater range which overlapped with that of the tiger, so it is possible, though unlikely, that they may once have sometimes occurred in the wild.