As Venn wrote in his 1880 article "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings," the diagram is a means of visualizing the relationships between two or more sets of things.
Or as the artist behind the doodle, Mike Dutton, explains on the Google website:
For example, one circle may contain things that are mammals. The other circle may contain things that have wings. The overlapping space that both circles occupy would consist of mammals that have wings.
The Doodle isn't the first tribute to Venn, who was born on August 4, 1834 and died on April 4, 1923. Others include the Venn building at the University of Hull in Yorkshire, England, and a stained glass window in a University of Cambridge dining hall.