A datapoint, instance, sample, or observation, is a unit of data in a dataset. When datasets are tabular, $x_{ij}$ usually represents the value of the $j$th variable (attribute) in the $i$th data point, where $i=1,2,...,n$ indicates the index of the variable and $j=1,2,...,p$ identifies the variable. This way, a dataset can be represented as an $n\times p$ matrix X, where the row (or vector) $x_i$ represents a datapoint that consists of the $p$ values of $x_{i1}, x_{i2}, x_{i3}, \dots , x_{ip}$ corresponding to each variable.