Ligers exist due to human influence. In natural conditions tigers and lions do not inhabit the same territory so do not have the opportunity to form such a species cross.
Ligers grow much larger than tigers or lions. This is because female lions and male tigers transmit a growth-inhibiting gene to their descendants. Being the offspring of a male lion and female tiger, the liger does not have the growth-inhibiting gene and grows much more (as explained on a BBC program).
A cross between a male tiger and female lion is called a tigon.