Originally, a right is an immunity to interference. Rights are "negative," i.e. they specify what I may do without your interference. Rights in the "positive" sense are altogether different: they are claims upon the wealth or service of another, e.g. the claim to medical insurance at another's expense. Rights in the original (and rational) sense arose only in the West in the Christian tradition.
A privilege is a benefit (in the wide sense) that one enjoys but is not the result of one's own work. There's nothing wrong with privileges; no one has control of where, when, and to whom he is born. Our task is to begin where we find ourselves and to grow from there. Read Viktor Frankl's "From Death Camp to Existentialism." Remember this, too: "From him to whom much is given, much will be expected."
If you want a short anwser-
A privilege is a certain entitlement to immunity granted by the state or another authority to a restricted group, either by birth or on a conditional basis. By contrast, a right is an inherent, irrevocable entitlement held by all citizens or all human beings from the moment of birth.