I'll try and explain it in easier terms:

• The world is about 40,000 kilometers (25,000 miles) around.
• A latitude/longitude value breaks that distance up into 360 degrees, starting at -180 and ending at 180.

This means that one degree is 40,000 km (or 25,000 miles) divided by 360. Lets do the math for both of those:

• 40,000 / 360 = 111
• 25,000 / 360 = 69

So, one degree is 111 kilometers, or 69 miles.

For fractions of a degree, you divide it by 10 for each decimal place, as @ChethanS's chart nicely demonstrates (in km):

   decimal places   degrees      distance
   0         1            111   km
   1         0.1          11.1  km
   2         0.01         1.11  km
   3         0.001        111   m
   4         0.0001       11.1  m
   5         0.00001      1.11  m
   6         0.000001     0.111 m
   7         0.0000001    1.11  cm
   8         0.00000001   1.11  mm

I'll try to explain it in different terms:

• Earth's equatorial circumference is about 40,000 kilometers (25,000 miles).
• A latitude/longitude value breaks that distance up into 360 degrees, starting at -180 and ending at 180.

This means that one degree is 40,000 km (or 25,000 miles) divided by 360:

• 40,000 / 360 = 111
• 25,000 / 360 = 69

(So, one degree is 111 kilometers, or 69 miles.)

For fractions of a degree, you divide it by 10 for each decimal place, as @ChethanS's chart nicely demonstrates (in km):

   decimal
   places   degrees     distance
   -------  -------     --------   
   0        1           111   km
   1        0.1         11.1  km
   2        0.01        1.11  km
   3        0.001       111   m
   4        0.0001      11.1  m
   5        0.00001     1.11  m
   6        0.000001    0.111 m
   7        0.0000001   1.11  cm
   8        0.00000001  1.11  mm