A population is the entire group of persons or objects about which you want to make inferences. A sample is a small portion of that population that you actually test and examine in order to collect data and make those inferences.
For example, suppose you wanted to test the average fasting blood glucose value of diabetics in the United States. It would be impossible to test all of them, so you would choose a small sample of them, usually through some random process. Then you would test only that sample, and from that, make an inference about the average glucose value of the whole country's diabetic population.
Choosing a sample that is representative of the population, however, is not an easy task. No matter how large a sample is, or how precisely the tests on that sample are carried out, the results are worthless if your sample is biased.