Post factum name for the type of battleship built by the world's navies between somewhere around 1870 and the development of the turbine-engined, all big gun dreadnought from 1906 onwards. Pre-dreadnoughts were powered by coal-burning reciprocating steam engines and tended to be around 10-15 000 tons displacement by the time of their rapid descent into obsolescence, and were capable of around 18 knots. They tended to carry rather heterogenous gun armaments - a typical late-era ship might carry four 12"/30cm calibre guns in fore and aft twin turrets, a dozen or so casemate-mounted guns in the 6"-9.4" (15-23 cm) range and a selection of smaller quick-firing weapons for fighting off torpedo boats.
The pre-dreadnought navies were a major element in the arms races of the time. The British Royal Navy maintained a policy of having at least as many battleships as the next two largest fleets (perm two of France, Germany and the USA; Russia, Italy, Japan and Austria were the world's other leading naval powers of the time) put together; the shifting patterns of alliances over the three decades in question made all sorts of permutations of opponents conceivable. However, few of the fleets ever saw action in earnest; the US Navy destroyed the decrepit Spanish colonial fleets at Cuba and Manila in short order during the Spanish-American war (triggered by the explosion of the battleship Maine), and the Japanese were easy victors over the Chinese in the Sino-Japanese war of 1894-5. The largest pre-dreadnought battles came in the Russo-Japanese war of 1904-5, when the Japanese under Admiral Togo beat first the Russian Pacific Fleet based at Port Arthur (effectively forcing a blockade; the blockaded ships were eventually destroyed by land-based artillery) and then, following the Russian Baltic Fleet's epic voyage half-way around the world, trounced it at the battle of Tsushima. The Mikasa, Togo's flagship, is the only remaining ship of the line of that era today, preserved in Yokohama harbour.
After the introduction of the faster and more heavily gunned dreadnoughts, the remaining pre-dreadnoughts took on a secondary role, mainly for coast defence duties; their most notable employment during World War I was in Churchill's abortive attempt to force the Dardanelles which led to the equally unsuccessful Gallipoli campaign, while a few fought with the German High Seas Fleet at Jutland. A few stayed in service still longer, and it was a German pre-dreadnought, the Schleswig-Holstein, which earned the dubious honour of firing the opening shots of World War II in Danzig harbour.
For photos and anorak details on the Mikasa: http://www.mindspring.com/~photon/kongo/mikasa.html