The mode of a dataset is the value that occurs most frequently. A dataset can be unimodal (one mode), bimodal (two modes), multimodal (several modes), or have no mode (all values occur equally often). The mode is the only measure of central tendency applicable to categorical data — you cannot compute a mean or median of colors, but the most frequent color is well defined.
For continuous data, the mode is the peak of the distribution — the value where the probability density function reaches its maximum. A bimodal distribution has two peaks and may indicate a mixture of two distinct subpopulations. The mode is easy to identify visually (the highest bar in a histogram) but can be unstable: small changes in data can shift the mode substantially.
The mode, median, and mean are the three classical measures of central tendency. For a symmetric distribution, all three coincide. For a skewed distribution, they diverge: the mode sits at the peak, the median in the middle, and the mean is pulled toward the tail. In Bayesian inference, the posterior mode (the maximum a posteriori estimate) is one way to summarize the posterior distribution as a single value.