I'm not native speaker and I was watching tv show "Friends" (s03e14). One of characters said "I'm the smallest person in the world" after complaining about his girlfriend's prosthetic leg. Can someone explain me what does this expression mean or is it just how it is? I could not found an answer in the internet.
This is a difficult question to answer via internet search alone. The character is using opposites for humour. The idiom you need to know to understand it is being the bigger person. You’ll get some google hits for that (unfortunately a lot of online advice telling you how to be the bigger person, but not an official definition of what it is that I could find).
For example if I was nastily complaining about someone behind their back to a friend of mine, the friend might tell me to "be the bigger person". That is, they mean complaining like that is beneath me and I should be mature/moral enough not to be so nasty/bitchy. You can also "be the bigger person" if you instigate an apology. The "bigger person" is high in moral fibre, forgiving.
The character is not only complaining about his girlfriend, he’s even picking on her disability. He is the exact opposite of the "bigger person" and he’s humorously accepting it by saying he’s the "smallest person".
a small person from A Dictionary of Confusable Phrases google book
morally mean, ungenerous people
As in your example, there is this sense:
One of characters said "I'm the smallest (mean spirited and/or ungenerous) person in the world" after complaining about his girlfriend's prosthetic leg.