Correlation measures the relationship between two variables. A correlation of 0 means there is no relationship between the variables, while a correlation of 1 suggests a perfect relationship. Conversely, a correlation of -1 means the variables are perfectly inversely related. For example, the correlation between exercise and weight is negative, since weight will decrease with more exercise. It is unlikely, though, that the correlation is perfect, so it is probably somewhere between o and -1.
Linear regression, which is related to correlation, is one of the most commonly used statistical tools in biology, economics and engineering. While correlation measures the relationship between only two variables, regression measures the relationship between two variables while taking into account what other variables are doing. In other words, regression controls for other variables. For example, a regression could measure the relationship between exercise and weight, controlling for diet and stress levels. This will give a clearer picture of the actual relationship between exercise and weight.
Though it is very basic, the mean is one of statistic's most powerful tools. Also known as the average, the mean allows for general comparisons between two disparate groups. For example, if you wanted to known how heights in Norway compared to heights in the United States, it wouldn't make sense to compare a few tall Americans to a few tall Norwegians. Rather, you would find the average height in the United States, and compare that to the average height in Norway.
The standard deviation measures the distance of a number from the mean, and is also essential for comparing distributions between groups. It might be, for example, that the mean height in Norway and the United States is similar, but that the United States has more very short people and more very tall people. This would show up in the standard deviation, which would be larger in the United States.