Progressive creationism is an interpretation of the biblical creation account which, like the day-age interpretation, attempts to harmonise the Bible with modern geology and ideas about the age of the earth, while at the same time rejecting atheistic evolution.
Progressive Creationism suggests that creation took place over a much longer period of time than the literal six day view held by Young Earth Creationism. This form of Old Earth Creationism aligns the days of creation, in order, with ages in prehistoric Earth. These days are taken to be indeterminate lengths of time, perhaps hundreds of millions of years. Many of the descriptions in Genesis can be seen as simple descriptions of complex scientific processes.
Within progressive creationism, the historical accuracy and inerrancy of scripture are accepted, as well as most findings of modern science. This is acomplished by taking the view that the Genesis account is given from the perspective of someone on the surface of the Earth. The appearance of light on the first day is taken to be the modification of the atmosphere to allow light to pass through to the Earth's surface. The universe, sun, Earth, and moon, etc are all believed to have been created in the event of Gen 1:1. The subsequent descriptions describe the transforming of the Earth into an inhabited world.
The order of the events in Genesis and it's many predictions of future discovery match remarkably well with the geological record. For instance, science has revealed that the early Earth was a water world lacking the large continents we have today. The gradual changes in the atmosphere described on days 1, 2, and 4 mirror the planet formation models predicting a thick initial atmosphere that thins out over time. By this, day four can be viewed as the final clearing of hazes from the atmosphere so that the heavens can be clearly seen. 
Progressive creationists generally believe that life on Earth emerged through the special creation of various kinds of plants and animals. Natural processes can describe many of the geological changes through history, but these events are guided by God. Micro evolution is sometimes included to one extent or another, in that God allows life to adapt to suit it's environment. But the common theme is that God is control over all of these processes.
Some have asked, "why would God use natural forces to perform His creative tasks?" The Bible often describes God controlling weather, astronomical events, and the actions of animals. By acting through natural forces, His works completed long ago are discoverable to us through scientific investigation.