A level C confidence interval for a parameter is an interval computed from sample data by a method that has probability C of producing an interval containing the true value of the parameter.
In the applet below we will construct a level C confidence interval for the mean (µ) of a population. Set the desired confidence level by clicking on the radio buttons to the left of the plot. Click the Sample button for a single SRS. Click the Sample 50 button for 50 SRSs. The dot marks the sample mean, which is the center of the interval. The lines on each side of the dot span the confidence interval. The total number of samples and number that "hit" (i.e., confidence interval did not contain µ) are shown on the right.