The full definition is standard deviation from the mean. The mean is the average of all observations, which is the sum of all the observational data (numbers) divided by the number of observations. Each individual observation (datum) will usually deviate from the mean by some amount, some data will be greater than the mean some smaller. If we add all these differences together and divide by the number of observations we will not get any sense of the spread of the data around the mean.
Therefore we square the difference between the data and the mean for each data value and add these together, then divide by the size of the dataset (number of observations). This is often known as the root mean square (RMS), but in statistics it's called the variance. The RMS or variance does give a good picture of the spread, but it's a squared value while the mean is not a squared value. To bring this spread into line with the mean all we do is take the square root. Now we have a very meaningful representation of the whole data. Variance is given the symbol σ2, so the standard deviation is represented by σ, and the mean is represented by μ. The whole dataset can be represented by the expression μ±σ, which simply means the data tends to lie in the interval [μ-σ,μ+σ].
For example, let's say we wanted to know the average height of adult males in a random sample of the population of a community. So we measure the heights of all the men in the sample and work out the average (mean). And we proceed to measure the standard deviation. The standard deviation would be expected to be small compared to the mean. So we have two statistics representing the whole sample. This allows meaningful comparisons to be made between different samples and different communities.
Provided observations can be reduced to numbers (numerical measurements), the mean and standard deviation method can be used for all sorts of situations, including those arising in dentistry.