The Dark Ages is a generalized term referring to Western Europe between the fall of Rome and the start of the Renaissance.
It was called “Dark” because a lot of knowledge was lost to the Western Europeans. People stopped maintaining libraries of knowledge and turned to matters of the spirit. Many old manuscripts were scraped clean of text and re-used to make copies of religious texts. People hard pressed to grow enough food to survive, and engaged in endless struggles with one another over territory, tribute, and religions aren’t predisposed to let their kids spend time studying ancient literature.
It was also “Dark” because the population contracted and disbursed, reducing many cities and towns in size and scope. Rome’s economic system enabled a substantial amount of trade which was needed to sustain concentrations of people. As the economy broke down and trade collapsed people had to disburse and population density was determined by the ability of local agriculture.
During this period there were plenty of Christians in Western Europe. Over time Christianity became the dominant faith, then it became a nearly-universal faith as anyone who would not convert was marginalized or killed (handful of exceptions such as Jews, but they were really minor exceptions). The centuries between the fall of Rome and the Renaissance in Western Europe can’t really be called “Pagan”.
Outside of Western Europe things remained much as they had for the previous millennia. Before Rome collapsed, the Roman Empire was split into two parts, and the Eastern part of the Empire, centered on Constantinople, survived a thousand years and retained much of Roman knowledge. In China and India the fall of the western half of the Roman Empire had little immediate impact. In the Americas and Africa south of the coast of North Africa there was no contact with Europe at all. The Middle East preserved and retained a lot of knowledge lost to the Western Europeans, conserving it until it would be reintroduced by returning Crusaders.
The Romans knew about certain engineering processes that were lost when the Western Roman empire collapsed. The knowledge of how to make concrete, for example, was forgotten. The mathematics and engineering the Romans used to build things like the aqueducts and the Roman Roads was lost. But people retained knowledge of metalwork, herbalism, geometry, and astronomy.
The Romans were more advanced engineers than their descendants but they were not more scientific. The Roman world was a superstitious land where gods and spirits controlled the world and the fates of humans. The Romans did not have the scientific method. They could not explain much about the world other than through their mythology. In this, they shared a worldview common to every person on the planet, until the middle of the 2nd millennium.