The ancient world's understanding of geography was both better and worse than popular imagination suggests. Better, because careful ancient geographers had a sophisticated grasp of large-scale geographical patterns; worse, because the specific accuracy of maps and distance estimates varied enormously.
Eratosthenes' geographical work positioned him as the founder of mathematical geography — using astronomical observations to fix locations on a spherical earth. His world map, reconstructed from descriptions, covered Eurasia and North Africa with reasonable accuracy on major features and significant errors on specific distances.
Strabo's Geography (1st century BC - 1st century AD), the most extensive surviving ancient geographical text, is a combination of mathematical geography, ethnographic description, and historical context. Strabo is at his best on regions he knows well (Asia Minor, Egypt, Greece) and less reliable on distant areas (India, sub-Saharan Africa, Britain) where he's dependent on earlier sources of variable quality.
The Roman military's use of geographical knowledge was practical and systematic: itineraries (road distances between points), regional surveys of grain production and population, and tactical descriptions of frontier terrain. The Tabula Peutingeriana — a medieval copy of a late Roman road map — gives some sense of what official Roman geographical knowledge looked like in schematic form.