Nuisance parameter: The parameter of the model in which there is no scienti?c interest but whose values are generally required (but in usual are unknown) to make inferences about those parameters which are of such type of interest. For instance, the aim might be to draw an inference m about the mean of the normal distribution when nothing certain is known about variance.
The likelihood for the mean, though, includes the variance, different values of which will lead to the different likelihood. To come over the problem, test statistics or the estimators for the parameters which are of interest are sought which do not rely on the unwanted parameter(s).