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I think the best way to describe the sampling distribution of the sample mean is through an example. Suppose we define a population as all company's listed in the S&P 500 Index on a particular day. We wish to estimate the average revenue of these companies by taking a simple random sample of size 10. We randomly select 10 companies from the index and compute the average revenue of each company as $1 billion. This is an example of a sample mean. The sample mean provides one estimate of the population mean . Now, suppose we performed this task, again, and again, for many simple random samples (i.e. picking 10 companies from the S&P 500, computing the average revenue of the 10 companies, replacing the companies into the S&P 500, and picking a new sample of 10 companies, computing the average revenue of the 10 companies, and so on and so forth). The frequency distribution of the resulting means from each simple random sample would be the sampling distribution of the sample mean. The sampling distribution of the sample mean is important in statistics because of the central limit theorem. The central limit theorem basically states that irrespective of the population's distribution, the samples distribution of the sample mean from that population will be approximately normal. Thus, even if a population is non-normal, the sampling distribution of the sample mean will be approximately normal.
thank you very much