To answer the original question, 1 minute of latitude is approximately 1 nautical mile. It actually varies a bit from exactly one mile. For example, one degree of latitude at the equator is 59.7 nautical miles, while near the pole it is 60.3 nautical miles.
But....1 nm for 1 minute of latitude is close enough!
Longitude, of course, is a different story. It varies from 60.1 nm per degree at the equator to 0.526 nm per degree near the pole. Which is why distance calculations on a nautical chart are always measured off the LATITUDE scale.