The Reliability Coefficient is a way of confirming how accurate a test or measure is by giving it to the same subject more than once and determining if there's a correlation which is the strength of the relationship and similarity between the two scores. If the two scores are close enough then the test can be said to be accurate and has reliability.
A reliability coefficient essentially measures consistency of scoring. An example could be done in which an individual is given a measure to determine their self esteem levels and then given the same measure again. The two scores would be correlated and the reliability coefficient would be produced. If the scores are very similar to each other then it can be said they are reliable measures that are consistently measuring the same thing, which in this case would be self esteem.