The mean is the average. Add up the values, and divide by the number of values.
The standard deviation (SD) quantifies variability. It is expressed in the same units as the data. It is often abbreviated as s. Prism computes the SD using a denominator of n-1, so computes what is sometimes called the sample SD rather than the population SD.
The Standard Error of the Mean (SEM) quantifies the precision of the mean. It is a measure of how far your sample mean is likely to be from the true population mean. It is expressed in the same units as the data.
The SEM is used to compute the confidence interval of the mean, and this CI is easier to interpret. If the data are sampled from a Gaussian distribution, you can be 95% certain that the interval encloses the population mean.
The variance equals the SD squared, and therefore is expressed in the units of the data squared. Mathematicians like to think about variances because they can partition variances into different components -- the basis of ANOVA. In contrast, it is not correct to partition the SD into components. Because variance units are usually impossible to think about, most scientists avoid reporting the variance of data, and stick to standard deviations. Prism does not report the variance.