Inferential statistics form one of the two essential components in statistical science (the other component is descriptive statistics). It is used to inform decision based on the currently best available evidence from a sample and to make generalizations outside the data at hand.
A researcher wants to determine the proportion of Hong Kong school children with habitual snoring. A sample of 3047 school children was contacted by phone. In this sample, 45 (1.5%) children were found with habitual snoring. We may use this percentage calculated from the sample to infer or in this case the true percentage in the population. The generalization process from a sample percentage to the population percentage is called inferential statistics.
A study was conducted to examine the association between capturing laughers with a camera and gender. We are certainly incapable of enumerating all individuals worldwide (the population) and ask if they like capturing laughers with a camera. What we can do is randomly draw a sample of individuals, with the hope of generalizing what we found from the sample to the population. This process is called inferential statistics.