A quick-and-dirty way of explaining the standard deviation is that it’s the “average distance from the average.” Normally, when you get take a bunch of statistical samples, they’re spread out over a range of possible values; roughly speaking, the width of this spread is the standard deviation.
For example: if I had 10 froobles, each of which was 10 cm long, then the mean length of my froobles is 10 cm and the standard deviation is zero (since each frooble happens to have the mean length, there’s no “spread” involved.) If, on the other hand, five of my froobles were 8 cm long and 5 of my froobles were 12 cm long, the mean length would still be 10 cm, but the standard deviation wouldn’t be zero any more, since none of the froobles would have the mean length any more. If five of my froobles were 5 cm long and five were 15 cm long, the standard deviation would be even bigger.
Here is a non-technical explanation of the standard deviation (written for journalists, not mathematicians.)