In the context of research, the reliability of a method refers to the extent to which, were the same study to be repeated, it would produce the same results. For this to be the case, samples need to be representative, questions or processes need to be uniform and data would generally need to be quantitative. Researchers need to be confident that if they repeat the same research and the result is different that what they are studying has genuinely changed and not just that their original method was not sufficiently reliable. If you take the example of opinion polls on people's voting preferences, if the support for parties changes by several points, the researchers (and their "customers") need to be confident that that is because people are really changing their minds about how they intend to vote and not simply that the research method is unreliable and therefore changes between polls are likely and unpredictable. If that were the case it would render their data useless.