If you are a retiring person, you avoid being at the center of attention. You can often be found in the library and other quiet places, and if someone compliments you, you're likely to blush and change the subject.
If you call someone retiring, it isn't necessarily clear whether you mean it as a compliment or something closer to a put-down. Usually, the word is used to describe someone who is shy or modest to a fault. But it can also be used to suggest that someone isn't arrogant, which is usually a good thing. And, of course, retiring can also refer to someone who stepped down from their last job and doesn't intend to work anymore.