Geologically speaking, uniformitarianism is the idea that geological processes (rates of erosion and uplift, etc.) are essentially the same today as they were in the unobservable past. According to this principle, we should be able to make accurate determinations about processes in the past simply by observing processes in the present. This principle is often summed up aphoristically in the phrase “the present is the key to the past.” A strict uniformitarian would look at a canyon with a river running through the bottom and see millions of years of slow, gradual erosion caused by that river.
Catastrophism is the idea that natural disasters (floods, earthquakes, etc.) can dramatically alter the surface of the earth very quickly and that we can be certain that at least some of the geological features we see today were formed rapidly during past catastrophes rather than by the slow, gradual processes of uniformitarianism. We must, therefore, take the possible effects of unknown catastrophes into consideration when studying the history of the earth’s surface. A catastrophist would look at the same canyon with the river running through the bottom and wonder if it was the result of gradual uniformitarian or rapid catastrophic erosion (like the canyon rapidly formed by the Toutle River washing out a mudslide following the Mt. St. Helens eruption in Washington State).
The uniformitarianism-versus-catastrophism debate is essentially this: how much can geologists rely on extrapolations of present-day geological processes when postulating the history and age of geological phenomena?
Of course, you won’t find the words uniformitarianism or catastrophism anywhere in the Bible. The Bible does say that Earth was inundated in a global deluge (Noah’s flood). Thus, any geological phenomena caused by gradual uniformitarian processes prior to that catastrophe were either eroded by the flood’s waters or else lost under the massive amounts of sedimentation deposited during the flood. We cannot necessarily rely upon uniformitarian reasoning when examining anything affected by this flood.