According to University of Glasgow Department of Statistics, a Confidence Interval is defined as:

~A confidence interval gives an estimated range of values which is likely to include an unknown population parameter (usually a population proportion or a population mean), the estimated range being calculated from a given set of sample data.

~If independent samples are taken repeatedly from the same population, and a confidence interval calculated for each sample, then a certain percentage (confidence level) of the intervals will include the unknown population parameter.

~Confidence intervals are usually calculated so that this percentage is 95%, but we can produce 90%, 99%, 99.9% (or whatever) confidence intervals for the unknown parameter

~Note:  For example, a 95% confidence interval (range of values), will contain the true population parameter (being estimated), 95% of the time. This is also called the  confidence level, degree of confidence, or the coefficient of confidence.

~This is a probability the confidence interval will contain the true population parameter being estimated, if this estimation process is repeated a large number of times.

~Note:  The population parameter is a constant (but unknown), so it will either fall in the interval each time we perform the estimation process or not.

~Therefore, it would be wrong to say that there is a .95 probability that it will, since the population parameter is fixed & is not a random variable...quite tricky...however, since we do not know if it does or not, a spectulaive guess on our part could use a probability interpretation. (even if there is no probability involved with its location)

~Example: let’s say that we have a 95% confidence interval for a population proportion as follows:    
.54 < p <.66.

~Suppose the true value of this parameter is .55 (unknown to us). In this case, the confidence interval does contain the true value of p.

~However, repeating this estimation process (from our sample data) a large number of times, we will produce many different limits (end points of our confidence intervals).

~Some may not contain .55.

~But we are sure that, in the long run, 95% of them will contain .55.

~There is a fine distinction between saying that & saying that there is a .95 probability that they contain .55, which is, technically, not correct...however, we could say that, based on a pure speculative guess....a bit confusing, to say the least

~Note: To find these easily using the TI-83, see the link, "Using the TI-83" on my Statistics page.