When statisticians are confronted with sets of data, they occasionally find there are data missing. This phenomenon has been given the name ‘Missingness’. Sometimes, a decision is taken that these missing data can be ignored, in which case they are classed as ‘Ignorable Missingness’. But on occasion, some missing data just can’t be ignored. In this case, it’s called ‘Non-Ignorable Missingness’.
For an example of how these two concepts might be applied in practice, see : ‘Maximum likelihood estimation of bivariate logistic models for incomplete responses with indicators of ignorable and non‐ignorable missingness’ in Journal of the Royal Statistical Society. Series C (Applied Statistics), Volume 51, Issue 3.