The phrase rocket launcher
can mean any one of a number of things. Here are a few of them.
Originally, the rocket launcher was any device used to, well, launch a rocket. If you build model rockets, you'll have at least one of these - a small tower or rod which holds the rocket upright, and optionally contains mechanisms for igniting the motors.
In military parlance, this applies to any weapon which uses unguided rocket-propelled projectiles. At the high end, artillery systems like the modern U.S. MLRS and the World War II-era German Nebelwerfer count as rocket launchers; large vehicles or towed artillery pieces which carry and fire unguided ballistic or direct-fire rocket weapons.
In modern times, however, there's a derivative of the military rocket launcher which has gripped modern imagination. Specifically, the shoulder-fired rocket launcher. Originally invented and used by armies as manportable weapons capable of engaging armored vehicles or bunkers, early rocket launchers include the German Panzerschreck and the American Bazooka. By the time World War II rolled around, both did a bang up job (haha) on bunkers, impromptu fortifications, and (in the Germans' case) the relatively light armor on Allied armored tanks.
Since the Cold War seemed to indicate that the next large-scale brouhaha was going to be tank-heavy (see Central Front) the development of shoulder-fired anti-armor weapons continued at a breakneck pace. The iconic Soviet RPG-7 and the American LAW exemplified two approaches. The Soviet model was a reloadable device which fired packaged rocket/grenade rounds; the American one was fully disposable, consisting of a single-shot launcher with the projectile packed inside it. Although both are 'rocket launchers,' the Soviet RPG (a descendant of the Panzerfaust) came to represent the image of a rocket launcher. Although it can be argued that more complex weapons such as MANPADS systems count, typically the word 'rocket' indicates an unguided weapon where 'missile' indicates a guided one. Hence, anti-aircraft weapons such as the Stinger, SAM-7 and relatives are more properly 'shoulder-fired missile launchers' rather than 'rocket launchers.' Of course, most modern shoulder-fired anti-armor weapons are guided also - the Milan, the Dragon, the Javelin, etc. - which means the pure 'rocket launcher' is limited these days to the smaller RPG and LAW derivatives. Ironically, the RPG-7 was an iteration of the RPG-2 - which was an almost direct copy of the German Panzerfaust, which was itself a disposable weapon.
Enter video games! The first person shooter game, once personal computers were powerful enough to support it, made the Rocket Launcher famous. Doom and its descendants, especially Quake and Halo, all featured a powerful weapon named, generically, Rocket Launcher. These became more than weapons - with the advent of Rocket Jumping in Quake, for example - and continue to form an indispensable part of the FPS genre. The recent release of Team Fortress 2 is a sequel, using the modern Half-Life 2 engine, to the original Quakeworld Team Fortress. The Rocket Launcher figured prominently in that game; in the new version, the rocket launcher is lovingly rendered in cartoonish but high resolution, and resembles a Panzerschreck on steroids.
The rocket launcher is synonymous with 'the weapon I couldn't realistically have' - which leads to excellent song lyrics such as If I had a rocket launcher, some son of a bitch would pay!