When you quantify something, you're putting it in numbers. If you're asked to quantify the fingers on your hand, you better say five.
If you like math, this word is for you: quantifying is counting or expressing something in numbers. Oddly enough quantify often comes into play when people are trying to count things that can't really be counted. When a doctor asks you to rate your pain on a scale of 1 to 10, he's asking you to quantify for your pain. Michael Jordan won 6 NBA championships, but you can't quantify what made him great: his drive and determination.