It's a reference to an old fairy tale. The idea is that the princess in the story is so delicate/sensitive that she can feel a pea under the mattress of her bed, and keeps complaining about it. So, saying that suggests that the person is very sensitive, or delicate, or perhaps that they complain a lot about little things.

The first one is a reference to an old and famous English fairy-tale. It's about a girl who was very, very sensitive because she was a princess. the princess symbolizes very sensitive and somewhat hard-to-be-around people. Pea, here, symbolizes a small thing that would not irritate, upset, or annoy a normal person. But a person with a princess complex would feel this "pea" and complain to everyone about it. He probably meant that you complain about every little thing that would not irritate a less sensitive person.