The capital ships of a navy are its "important" warships; the ones with the heaviest firepower and armor. There is usually no formal criterion for the classification, but it is a useful concept when thinking about strategy, for instance to compare relative naval strengths in a theater of operations without having to get bogged down in the details of tonnage and gun diameters.
In the 20th century, typical capital ships would be battleships, battlecruisers, heavy cruisers, and aircraft carriers. In the 21st century, the aircraft carrier is the last remaining capital ship, with firepower defined in decks available and aircraft per deck, rather than in tubes and calibres.
Before the advent of the all-steel navy in the late 19th century, a capital ship was a warship of the first, second or third rate:
1st Rate: 100 or more guns, typically carried on three or four decks. Four-deckers tended to have problems with the waterline and the lowest deck seldom was able to fire except on the calmest of seas.
2nd Rate: 90-98 guns
3rd Rate: 64 to 80 guns (although 64-gun third-raters were very small and not very numerous in any era).
Frigates were ships of the fourth or fifth rate; a corvette was a ship of the sixth rate.
Fictional capital ships
In the Star Wars universe, "capital ship" refers to any starship 100 meters or longer.
Capitalship was a general term for any military starship with a length greater than 100 meters.
For example, the Sienar Fleet Systems GAT-12 Skipray Blastboat was considered a capitalship because of its heavy armament, despite being a mere 25 m in length and operating primarily in the role of a starfighter.
Many capitalship classes also served as carriers and were able to deploy starfighters, landing craft, and other resources as required.
A ship without a particle shield, however it is achieved, could easily be heavily damaged by a small grain of sand if the ship runs into the grain of sand at a significant fraction of the speed of light.
Some ships may be equipped with a particle collector that will gather particles and atoms from space for use as fuel, and such systems can eliminate the need for fuel, but they require a large amount of area to be exposed to space and are not suitable for small ships or fighters.
Capitalship weapons is a very broad category of weapons that includes any direct firing weapon that is not considered to be a point defense weapon.