A reaction control system (RCS) is a collection of components aboard a vehicle which uses reaction thrusters to produce translational or rotational velocity changes. In other words, to spin or push the vehicle around. Although in some cases the RCS thrusters use rocket motors - the Apollo spacecraft, and the Space Shuttle, for example - in others, they might consist of cold-gas thrusters which simply vent pressurized gases to produce the required impulse. Operations that don't involve combustion, although not nearly as energy efficient, make the construction and operation of the thruster easier and safer! Combustion systems, in order to minimize complexity, will typically utilize hypergolic fuels. The concomitant typical toxicity and corrosive nature of these fuels, as well as issues managing them, are usually offset by not needing to provide systems for their ignition for each impulse.
Although RCS are generally used in a vacuum because they're the only option, they can be used within the atmosphere. It's just that generally any vehicle maintaining powered flight can much more efficiently and/or easily make changes to its velocity vector or attitude by utilizing aerodynamic means or manipulating that primary power system. If there is a separate system for utilizing the power generated by the main engine, that may be described as a reaction control system; for example, on VTOL aircraft just as the Harrier jumpjet, below speeds where the atmospheric controls are effective, engine thrust can be redirected through various venting systems, sometimes at the end of relatively long ducts, in order to provide attitude and translational control
Vehicle attitude control, for longer flight times, is generally done with some form of system that does not require consumable fuel, such as reaction control wheels or control moment gyroscopes. The RCS is generally still useful, as not only can it be used if those systems fail, but torque management systems can reach saturation, requiring an RCS burn to provide a balancing force against which they can 'dump' their stored momentum. This procedure (balancing the internal attitude control system impulse against RCS impulses or other systems such as magnetorquers) is called a momentum dump.
RCS can be found aboard both manned and unmanned spacecraft. They can also be found on very high speed systems that operate within the atmosphere, where more complex or less effective systems are not feasible. Some designs of antiballistic missiles (ABMs) use small consumable reaction control thrusters - much like shotgun shells - for their final few fractions of a second before intercept, when the actuation time required for any other form of control system is too long.