Before modern navigational methods were available, the navigator incorporated his estimation of these forces (wind, current, helmsman error...) in his DR plot. The DR plot was often the only method used if, for example, the sky was overcast and a celestial observation could not be made.
Before the development of the chronometer, dead reckoning was the primary method of determining longitude available to mariners such as Christopher Columbus and John Cabot on their trans-Atlantic voyages.
There is some controversy about the derivation of the phrase. It is popularly thought to come from deduced reckoning and is sometimes given in modern sources as ded reckoning. However, according to the Oxford English Dictionary, the phrase dead reckoning dates from Elizabethan times (1605-1615).
The folk etymology from deduced is not documented in the OED or any other historical dictionary. Dead reckoning is navigation without stellar observation. With stellar observation, you are "live", working with the stars and the movement of the planet. With logs, compasses, clocks, but no sky, you are working "dead".