Here is the dilbert’s cartoon on “randomness” concept..It basically summarize the concept, and I really like it.
When discussing single numbers, a random number is one that is drawn from a set of possible values, each of which is equally probable. In statistics, this is called a uniform distribution, because the distribution of probabilities for each number is uniform (i.e., the same) across the range of possible values. For example, a good (unloaded) die has the probability 1/6 of rolling a one, 1/6 of rolling a two and so on. Hence, the probability of each of the six numbers coming up is exactly the same, so we say any roll of our die has a uniform distribution. When discussing a sequence of random numbers, each number drawn must be statistically independent of the others. This means that drawing one value doesn’t make that value less likely to occur again. This is exactly the case with our unloaded die: If you roll a six, that doesn’t mean the chance of rolling another six changes.