Reliability is the term commonly used in research for consistency of measurement. Obviously, consistency is a prerequisite for accuracy. To be considered reliable a measure must have two characteristics.
First, it must give similar results every time it is used to measure the same thing. That sounds obvious, but if you're estimating intelligence, however you want to define it, you will not find an intelligence test which will estimate the same IQ every time it is given to the same person. You then have to determine whether the test you want to use gives similar enough results to be useful.
The measure also should give similar results no matter who does the measuring. No measure satisfies that ideal entirely, but again estimation of reliability coefficients will establish if a measure you're interested in gets close enough to that ideal.
When you're using paper-and-pencil tests, like intelligence tests, achievement tests, or aptitude tests, a couple of extensions of these principles are important. First, all the items on the test should be measures of the same thing. A specific class of reliability coefficients can help you evaluate a test's success in satisfying that criterion.
The second extension involves the common pracice of producing tests in two forms, so that the test can be given twice to the same person without the results of the second administration being affected by experience with the first. The different forms of the same test should produce the same results, assuming that nothing happens between the administration of the two forms which might affect the results. Again, reliability coefficients can be calculated to estimate how well a test satisfies this criterion.