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A runaway process is a process with the characteristic that its own progress causes the process to progress faster. It is a process that incorporates positive feedback, i.e., it creates conditions which have a positive effect on its progress. This leads to exponential growth of something, i.e., after a unit of time, something has grown by a some constant ratio. Such a process always reaches some physical condition that slows it or shuts it down, sooner or later. For example, runaway fusion inevitably uses up the available fuel (the runaway quality typically making this happen in a very short time). Technological design often requires avoiding positive feedback and runaway processes. Examples of runaway processes within astrophysics:
Two ordinary-life processes that fit the definition of runaway process are population growth and investments that offer compound interest.