Heat maps are a graphical representation of data on a map through the use of colors to indicate the density of something. For example a heat map could be used to show the level of unemployment in different states.
The HeatMapAPI is an API that enables anyone to create their own heat maps. If you wish to use the HeatMapAPI the GeoChalkboard blog has a good tutorial on how to create a heat map with the API and Google Maps called Density Mapping in Google Maps with HeatMapAPI.
The GeoChalkboard tutorial shows you how to create a heat map using data showing Starbucks closure of 600 stores.
One alternative to the HeatMapsAPI is using Google's Visualization API with Google Spreadsheets. Ouseful has a good example of a heat map of Olympics medal winners created using Google Spreadsheets.
The Google Maps creation website Maker! also has an option to create coloured heat maps (Choropleth Maps).