Non-Gaussianity means a departure from Gaussian statistics of a physical quantity or random field. Higher connected correlation functions describe such departures. Primordial non-Gaussianity concerns the initial cosmological perturbations.
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Non-Gaussianity refers to the deviation of a probability distribution from a Gaussian (normal) distribution. In a Gaussian distribution, data is symmetrically distributed around the mean, with most values clustering around the center and fewer values appearing as you move farther from the mean. The characteristics of a Gaussian distribution can be completely described by its mean and variance. When data exhibits non-Gaussianity, it means that its distribution does not follow this normal pattern.