Here's a great definition provided by the National Council on Public History:
"Public history describes the many and diverse ways in which history is put to work in the world. In this sense, it is history that is applied to real-world issues. In fact, applied history was a term used synonymously and interchangeably with public history for a number of years. Although public history has gained ascendance in recent years as the preferred nomenclature especially in the academic world, applied history probably remains the more intuitive and self-defining term".
For additional information on who does public history,
how public history is used, how public history is different from "regular" history, etc., check out the full web page.
Image from: The British Museum