A battlecruiser (old United States Navy hull classification code CC) is the intermediary step between a heavy cruiser and a battleship. First postulated on shortly after the launch of HMS Dreadnought in the first decade of the 20th Century by then-First Sea Lord of the Royal Navy Sir Jackie Fischer, the battlecruiser concept was designed to create a fast ship with overwhelming firepower that could scout ahead of the main battle line and overpower enemy cruisers, but never engage the enemy battle like; this was due to the near-total absence of protective armour in the battlecruiser's hull that could withstand battleship-calibre shells. All British-designed battlecruisers from the first one, HMS Invincible, to the last, HMS Hood, pretty much followed that same concept. Battlecruisers designed by Allied nations such as the United States' Lexington-class followed this trend.
The Germans took a slightly different route once they came to understand the idea. While maintaining good armour on their battlecruisers, starting with SMS Von Der Tann, they sacrificed gunpower to reduce weight and allow greater speed to be obtained while maintaining survivability. This was proven to be an excellent choice to make as the Battle of Jutland showed in 1916; in that battle, Britain lost three battlecruisers (HM Ships Invincible, Indefatigable and Queen Mary) and nearly lost a fourth (HMS Lion) due in part to the lack of decent protective armour; plunging shellfire struck their main powder magazines and caused the ships to be destroyed by massive explosions. Only one German battlecruiser, SMS Lützow, was sunk in that battle...but only after taking incredible levels of damage from the main British battle line.
As was proven at the Battle of the Denmark Strait in 1941, even an "improved" battlecruiser such as HMS Hood, which had been redesigned after Jutland to incorporate the lessons of that battle, was still not suited for direct combat against a true battleship; she was sunk by a potential strike in her aft main magazine by a shell from the German battleship Bismarck shortly after the two ships engaged.
Fortunately for the one other nation that adopted the battlecruiser concept, Japan, the lone class of such ships were rebuilt in the 1920s and 1930s to become the Kongō-class fast battleships. Such a decision allowed Kongō and her sisters Hiei, Haruna and Kirishima to serve quite well in the Pacific Theatre of World War Two.
Today, the concept of "battlecruiser" is most often applied to the Russian (ex-Soviet) Project 1144 (or "Kírov") class nuclear-powered missile cruisers; in Russia, these ships are classified simply as "heavy nuclear-powered guided missile cruisers".