A heatmap is a color-coded grid added to a map. The colors usually range from cool colors, such as blue, to hot colors, such as yellow, orange, and red. Heatmaps represent point data in one of two ways: density or intensity. In a density map, the grid is colored red when multiple points are in close proximity of each other and blue when dispersed. High concentrations of points create the heat. In an intensity map, points are assigned a value or an intensity score. The higher the score or intensity, the hotter the color in the grid at the location of the point; inversely, the lower the score, the cooler the grid color at the point location.
Heatmaps are created by placing a grid over the map and calculating the points within an area through a process called Multivariate Kernel Density Estimation. For a detailed explanation and the exact formulas used, you can visit http://en.wikipedia.org/wiki/Multivariate_kernel_density_estimation.