The mean of a random variable weighs each possible outcome according to the probability that it will occur. Compare this to the sample mean which weighs each possible outcome equally. The mean (expected value that E will take) is the sum of all outcomes, each multiplied by its probability. It is a running average of the random variable's expected value. The results that are more likely to occur are weighted more (because they have a higher probability) so the running average (mean) is closer to those values.
where the p's indicate the probability of that x occurring.