Reliability or reproducibility in statistics refers to consistency in measurement: the capacity to produce the same result for two identical states; or, more operationally, the closeness of the initial estimated value(s) to the subsequent estimated value(s).
Reliability of statistics or statistical indicators is a necessary (but not sufficient) condition for their faithfully measuring the reality they have been designed to represent. It should not be confused, however, with validity, measuring what one intends to measure: it is quite possible to measure reliably a completely invalid aspect.