Rocket science
Earth is the cradle of mankind, but man cannot live in the cradle forever — Konstantin Tsiolkovsky
5...4...3...2...1...[word removed in accordance with Citizendium family-friendliness policy] — Reported to be the way the children of rocket scientists learned to count
Rocket science is an everyday term for astronautics, or astronautical engineering, the branch of engineering that deals with vehicles that travel in whole or in part through outer space. It is compared and contrasted with aeronautics, the field that covers vehicles travelling within the Earth's atmosphere. There are naturally overlapping areas within the two disciplines, so the modern tendency is to combine the two as aerospace engineering.
The term is also used when speaking of a relatively easy task being made difficult through opposition or incompetence. "This isn't rocket science, folks!"
Rocket scientist describes an aero/astro engineer. It is also used admiringly to refer to any extraordinarily intelligent person, or sarcastically to describe someone who has done something stupid.
Confusion in the actual term
"Rocket", per se, is either a relatively simple military device, firework, etc.; see unguided rocket, and multiple rocket launcher for some of the more lethal aspects. Indeed, see counter-rocket, artillery and mortar (C-RAM) for means of defending against certain of the military systems.
In more complex space launch vehicles (SLV) and in many, but not all, guided missiles, the rocket motor is a propulsion subsystem. Many SLVs and missiles have multiple rockets, which variously may be clustered into groups firing in parallel, rocket systems that fire in series or stages (i.e., step rocket), and various hybrids of "booster" and "sustainer" (e.g., Atlas (missile).
Historical rocketry
Possibly first developed for entertainment, but then as powered "fire arrows", the first rockets were invented in China or Korea, probably in the 13th century. They evolved for several hundred years, but were wildly inaccurate, and served more as a psychological than kinetic weapon. With much more knowledge of aerodynamics, it is possible to use fins to give some stability to an unguided rocket, but they remain far less accurate than firearms.
Some improvement came with Sir Henry Congreve's invention of a stabilizing stick that protruded from the rear of the rocket, but, while "the rockets' red glare" stirred Francis Scott Key to write "Star-Spangled Banner" as he watched the night bombardment of Fort McHenry, the rockets actually did very little damage. There were improvements, but it was really not until the Second World War were the characteristics of unguided rockets understood well enough to make them into useful weapons.
Among their greatest advantages was the ability to be fired from lightweight frameworks or tubes, rather than gun barrels that had to withstand pressure. If the goal was to to spread warheads over a wide area, suppressing infantry, perhaps detonating mines, and killing the crews of artillery, multiple rocket launchers made good use of the inherent inaccuracy. It was practical to build a short-range tube-guided rocket, and, especially when coupled to the Munroe or "shaped charge", the simplest form of explosively formed projectile, soldiers acquired handheld weapons that could defeat light armor.