It's a derogatory, slang term which means one of two things.
Meaning #1 is "hick" or "hillbilly". By the time of Constantine Christianity was the religion of the urban elite and the only people who hadn't converted were those who lived out in the boondocks.
Meaning #2 is "civilian"- that is to say, someone who hasn't enlisted in the army of Christ.
Modern Pagans tend to define Paganism as a Nature religion. Well, yes, up to a point. But Paganism isn't one single thing. Everything that happened in Western religion before the advent of Christianity is covered by the term. The builders of Stonehenge were Pagans but so were Plato and Aristotle.
Athena is not a Nature Goddess.
The Wiccan myth (based on the writings of Margaret Murray) insists that Paganism flourished as an underground movement (stigmatized as Witchcraft) all through the Middle Ages. The most one can say about this is that there is hardly any evidence for it.
What did happen was that the Church assimilated Pagan practise and belief. The Winter Solstice turned into Christmas. Gods and Goddesses- like Brigit- were rebranded as Christian saints.
Medieval Catholicism- especially away from the cities- was a continuation of Paganism by other means.
The Renaissance saw a passionate revival of interest in Pagan antiquity. Shakespeare- a typical Renaissance author- is steeped in Pagan mythology (which he mainly got from Ovid.)
Modern neo-paganism is a child of the romantic movement. Its attitudes- a hatred of rationalism and industrial civilisation and an idealisation of Nature- exist, almost fully formed, in the work of early 20th century authors like Kenneth Graham and Algernon Blackwood.
This essentially literary movement came together with the Magical revival (also a product of romanticism) to give birth to Wicca- the first (or at least the first successful) neo-pagan religion- in the middle of the 20th century.