Here are couple of references for CI. Without getting too technical on the computations, these provide the motivation, "how to" and more importantly, the interpretation of the CI.
The key lines for me:
"The theoretical basis for the calculation of a CI includes the assumption that (he study can be repeated many times. Each time, different results would be obtained through the selection of a slightly different sample of patients from the population (sampling variability). Each trial would therefore also produce a different 95% CI. If the trial were performed 100 times, then, on average, 95 of the 95% CIs calculated would contain the true value (and 5 would not). In practice, however, we usually perform a study only once. Once we actually perform a trial, and calculate a single 95% Cl, the true value either lies within this confidence interval or it does not. Therefore, in referring to the particular results from a single study, it is not correct to state that there is a 95% chance or probability that the true value lies within the CI. It is correct to say that if the true value lies outside the 95% CI, the likelihood of obtaining the data observed in the study is 5% or less."
Emphasis is mine.
