What, exactly, is the "precious innocence" which is introduced in chapter 7 of The Great Gatsby?

The incident you refer to occurs when Nick and Jay are both at the Buchanans' house at Daisy's invitation. Nick suspects that the couple, who are now involved in a fully-fledged affair, wish to come out publicly with the truth and cause a scene, as he states:

Something was up. And yet I couldn’t believe that they would choose this occasion for a scene ...

Tom Buchanan, who had been on the phone soon after Nick and Jay's arrival, came in briefly and left again. Jordan Baker suggested that he had been speaking to his mistress. Once he was gone, Daisy kissed Jay on the mouth and Jordan called her 'a low, vulgar girl.' Daisy said that she didn't care and sat down on the couch.

At this point, a nurse who had just recently dressed herself came into the room, leading a little girl. Daisy reacted by crying out:

“The bles-sed pre-cious! Did mother get powder on your old yellowy hair? Stand up now, and say—How-de-do.”

Daisy was speaking to her daughter and then introduced the shy child to her guests. Jay was surprised on seeing the child, almost, as Nick suggests, as if her presence finally convinced him that the child actually existed, for he never, apparently, thought of her as real.

Both Daisy and Jay's actions are significant in this excerpt. Daisy has an obviously distant relationship with her daughter. Her response is not convincing and it seems that the child is a mere object to be presented to an audience. Her condescension to her child is bred from her idea of how a mother should be, but comes across as false and forced. Her entire response centers around how she presents her child, as she herself says, when the child tells her that she got dressed before lunch:

“That’s because your mother wanted to show you off.” Her face bent into the single wrinkle of the small, white neck. “You dream, you. You absolute little dream.”

Even the fact that Daisy does not recognize the child's uniqueness and rather sees her as a copy of herself suggests her self-absorption. Once the child has achieved her purpose, she is sent off with the nurse, almost like a precious object which is put back into its wrapping and box after it has been shown off. Even the child's name, 'Pammy,' suggests something to play with.

Jay's surprise at seeing Pammy is an indication of the fantastical nature of his ideal. He wishes to recreate the past, but now has to accept the difficult reality that Daisy has created a life for herself—she is married and is a mother. The past cannot just be revived on a whim.

The incident also foreshadows what is to happen later, when Jay, in his confrontation with Tom Buchanan, will be exposed to an even greater truth.