The hard science fiction ( or "hard science" when no misinterpretation is possible) derives its name from the "hard sciences" (such as Mathematics, Chemistry, Physics, Astronomy etc) where logic and mathematics prime as opposed to the "soft sciences" ( Psychology, Sociology, History etc). The distinctive qualities of such sort of science fiction is the plausibility of the scientific principles involved. Very often the authors of such novels are scientists and the difficulty for them resides in writing an interesting story as well as an accurate one.

Example of such novels include (you may disagree):

Jules Verne : From the Earth to the Moon (1865)
He even choosed the Houston site to build his canon to shoot at the moon for the same reasons the NASA did.
Fred Hoyle : The Black Cloud (1962)
A black cloud approaches the earth...
Arthur C. Clarke: Rendezvous with Rama (1973)
Hard science fiction at least for the human side.

m_turner suggests:
Robert L. Forward, Stephen Baxter and Gregory Benford.

Transitional man also suggests:
Charles Sheffield, Catherine Asaro, John Cremer and Larry Niven, Hal Clement and also Geoffrey Landis.

Sverre mentions Isaac Asimov, Of course! How could I have forgotten him ?