One nautical mile is 1.1507794480 statute miles. The two are close enough that they are constantly confused and far enough apart that the confusion matters — a fifteen per cent error in a distance at sea or in the air is not a rounding detail.
About the units
The statute mile is a land unit, defined by English statute in 1593 as eight furlongs and now fixed at exactly 1,609.344 metres. The nautical mile is a navigational unit derived from the Earth's geometry, one minute of latitude, standardised at exactly 1,852 metres. They have nothing in common except the word mile, and the shared name is purely historical accident. The distinction is old enough that English has kept both, but many languages use a separate word for the nautical unit precisely to avoid the ambiguity — the Scandinavian languages, for instance, use sjömil and distinguish it clearly from the land mil.
The exact factor
Since both are exactly defined in metres, the ratio is exact too: 1,852 ÷ 1,609.344 = 1.15077944802354... The reverse is 0.868976241900648. A useful mental approximation is that a nautical mile is about fifteen per cent longer than a statute mile, or seven-sixths of one. The corresponding speed units follow the same ratio: 10 knots is 11.5 mph, and 60 knots is 69 mph — which is where the old rule of thumb about knots and miles per hour being "about the same" comes from, and also why it is dangerous over long distances.
Where you meet this conversion
Aviation is where the two collide most often. Aircraft performance figures, range and airway distances are in nautical miles, while general aviation in the United States sometimes quotes statute miles, and visibility on American aerodrome reports is in statute miles while everywhere else uses metres. Boating shows the same split: coastal charts and GPS units are in nautical miles, but a boat's advertised range or a lake's dimensions may be in statute. Getting the wrong one on a fuel calculation is a well-documented category of accident.