[Craig Roys]

Resident Physics teacher here.

The previous posts are correct: 1 g = 9.81 m/s/s
It is just a way to compare apparent weight to actual weight on earth. Typically used in cases using circular motion (jet, space shuttle, rollercoaster, etc.). To say you are experiencing 3 g's would be to say that you feel 3 times heavier that you would standing still on earth because you are experiencing 3 times earth's acceleration due to gravity (i.e. a 150lb person experiencing 3 g's feels as if they weigh 450lbs).
This apparent extra weight comes from forces (in addition to gravity) acting on an object - usually centripetal force.

One last nit-picky thing. g's are represented with a lower case g so as not to be confused with the gravitational constant: G=6.67x10^11 N*m^2/kg^2.

Hope that helps.