Introductory Statistics - Estimating Means with Confidence

For my Elementary/Introductory Statistics class we are studying Confidence Intervals for Means. It deals with parameters for populations, statistics (a.k.a. estimates) for samples, using the formula for Standard Error of a Sample Mean, the formula for Standard Error of a Sample Mean of Paired Differences, and other formulas. My only questions is, what is the meaning behind the t* multiplier used for finding the confidence interval for a population mean? And how am I supposed to use the Degrees of Freedom in the table for t-distribution in order to find the necessary t* multiplier to use in my formula for Calculating a Confidence Interval for a Population Mean? This particular formula is written as x-bar + and - t* X s.e. (x-bar), which is x-bar + and - t* (s/sqrt of n). Thank you very much for the help!