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A boxplot, or box-and-whisker plot, is a graphical representation of a dataset that displays its central tendency and variability. It shows the median, quartiles, and potential outliers, providing a visual summary of the distribution. The box represents the interquartile range (IQR), which contains the middle 50% of the data, while the 'whiskers' extend to the smallest and largest values within 1.5 times the IQR from the quartiles.

Quartiles are values that divide a dataset into four equal parts, helping to understand its distribution. The first quartile (Q1) is the median of the lower half of the data, the second quartile (Q2) is the overall median, and the third quartile (Q3) is the median of the upper half. These values are essential for constructing a boxplot, as they determine the box's edges and the whiskers' extent.

Outliers are data points that significantly differ from other observations in a dataset. They can skew the results and affect statistical analyses. In the context of a boxplot, outliers are typically identified as points that lie beyond 1.5 times the IQR from the quartiles, and they are often represented as individual dots outside the whiskers, indicating their potential impact on the overall data interpretation.