Summary
The real difference between reliability and validity is mostly a matter of definition.
Reliability estimates the consistency of your measurement, or more simply the degree to which an instrument measures the same way each time it is used in under the same conditions with the same subjects.
Validity, on the other hand, involves the degree to which you are measuring what you are supposed to, more simply, the accuracy of your measurement. It is my belief that validity is more important than reliability because if an instrument does not accurately measure what it is supposed to, there is no reason to use it even if it measures consistently (reliably).
Reliability refers to constancy or consistency in measurement. Reliable procedures are repeatable and replicable. Validity is the credibility or genuineness of results.