The Simulation Argument is one of a number of ideas relating to the Simulation Hypothesis. The important distinction between this argument and earlier simulation models has been the addition of a proposed method of engineering Simulated Reality through the use of computers and the assumption that the conscious beings with the simulation are themselves simulated, rather than merely "brains in a vat"
Nick Bostrom's paper Are You Living in a Computer Simulation? argues that one of following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor simulations is false, unless we are currently living in a simulation.
Other proponents such as John Barrow have suggested that if we are living in a computer Simulation we may observe "glitches" in the our programmed environment due to the level of detail being compromised to save computing power. Alternatively, the Simulators may not have a full understanding of the Laws of Nature which would mean over time the simulated environment would drift away from their stable state. These "glitches" would probably be identified by scientists scrutinizing nature using unusual methods of observation.
Bostrom, Nick (2001,2003) *Are You Living in a Computer Simulation Philosophical Quarterly (2003) Vol. 53, No. 211, pp. 243‐255.
Bostrom, Nick (2011) *A Patch for the Simulation Argument Analysis, Vol. 71, No. 1 (2011): 54-61