Wikipedia
In statistics, the Q-function is the tail probability of the standard normal distribution ϕ(x). In other words, Q(x) is the probability that a normal (Gaussian) random variable will obtain a value larger than x standard deviations above the mean.
If the underlying random variable is y, then the proper argument to the tail probability is derived as:
$$x=\frac{y - \mu}{\sigma}$$
which expresses the number of standard deviations away from the mean.
Other definitions of the Q-function, all of which are simple transformations of the normal cumulative distribution function, are also used occasionally.
Because of its relation to the cumulative distribution function of the normal distribution, the Q-function can also be expressed in terms of the error function, which is an important function in applied mathematics and physics.