The basic conflict was that more scientific knowledge was being acquired and some aspects of this knowledge came into conflict with the teachings of the Christian church.
The most obvious example of this was the theory of evolution as made popular by Charles Darwin. This theory ("The Descent of Man" was published in 1871) called into question the idea that God had created all things in their current forms. And more generally it called into question the scientific accuracy of the Bible.
Another way in which this happened was that Charles Lyell found a great deal of evidence that cast doubt on the idea of Noah's flood and on the idea that the Earth was quite young (as determined by Bishop Ussher).
Up until the 1860s, the harmony between science and faith continued to be mainstream, but there were some earlier threats from working-class radicals who saw an avenue for using certain versions of science for political ends. For instance, some forms of the sciences from France saw God in a much diminished role in the universe. British men, especially geologists, made discoveries which threatened the literal meaning of the Book of Genesis in the Bible. And, of course, Darwin's "Origin of the Species" posed threats for religious fundamentalists who believed in the existence of a designing God.
British scientists such as Thomas Huxley and John Tydall, who argued for the superior authority of science over religious or non-rationalist explanations. Thus, they argued against clergymen being involved in the study of science, contending that science should be carried out by specialist experts instead. However, publishers with explicit religious credentials continued to publish works on the sciences. So, while there were contentious debates among the intellectuals, the majority of the British population reconciled science easily with their religious beliefs.
The discovery that the earth was not young also brought with it the discovery that the history of the earth could basically be summarized as a series of cataclysmic deaths. Dinosaur bones had recently been discovered, and this idea that a whole, dominant species could eventually go extinct began to worry some Victorians, as it was a common belief that as humans, they were chosen by God to inherit the earth and were therefore the highest and best form of life, and nothing would come after them.