A capital ship was a starship classification used by Starfleet. California-class vessels were not considered capital ships, but Luna-class ships were. (LD: "Strange Energies", "An Embarrassment Of Dooplers")
In 2381, Admiral Alonzo Freeman told Captain Carol Freeman that Starfleet was impressed by how she handled the Pakleds, and that she could be due for a promotion to commanding a capital ship so long as she kept a clean record. (LD: "Strange Energies")
Only officers of capital ships were invited to the Command Conference on Starbase 25. (LD: "An Embarrassment Of Dooplers")