Purring is the sound that cats produce to express happiness but also sometimes when they are ill or having a bad time. This tonal buzz is not produced by any particular part of their organism, they make this noise in the inhaling and exhaling proccess.
It is not 100% clear if tigers and other big cats can actually purr.
It was believed by experts that only domestic cats could purr, but recent studies have demonstrated that 'roaring cats' of the panthera genus like tigers, lions, jaguars and leopards produce a sound similar to purring but only when exhaling air.
The reason why big cats are not able to purr is the difference in an organ called the hyoid that in their case is ossified and does not let them purr but produces their characteristic roar instead.