No official in-universe use, but they should be data storage devices according to Michael and Denise Okuda

I asked Michael and Denise Okuda (TNG production and art designers) this question ten minutes ago at the Star Trek 50th Anniversary Celebration in Las Vegas.

MICHAEL: That's a darn good question.

He then explained that, out-of-universe, these orange plates are props left over from The Motion Picture. Circuit designs were painted on them for TNG.

In-universe, he said that no specific function had ever been assigned to the plates. There was talk at one point amongst production personnel and/or set designers that they might serve as PADD-style devices (data display devices or readers, but smaller and thinner than PADDs). But he insisted that no official purpose had ever been assigned to them by any designers or writers. He did say that, in retrospect, they should probably be data storage devices.