Mean is the sum of variables divided by the number of variables. When someone talks about "average" of something, they are most likely talking about the mean.
This is another type of average, but people use this less often than the mean. Median is the middle value of all the variables. In order to find the median, you have to list the numbers (variables) from the smallest to the largest and find the value that is in the middle.
Standard deviation, σ, tells us how much the data is spread out. It's the square root of the variance. Variance, σ^2, is when you find the difference from the mean of each sample, square it, and take the average of the differences of all the samples. We use standard deviation more often than variance because the units of the standard deviation are the same as the units of the sample itself.
Low standard deviation tells you that data is close to the mean, where high standard deviation shows that data is spread out from the mean.