Sampling is the process of selecting individuals/items/trees/things from a larger population.
Often it is not possible to take data from each and every individual.
We use a sample to make inferences about the whole population.
A simple random sample is a subset of individuals/items/things chosen from a larger population.
Each individual is selected randomly, such that each individual has an equal probability of being selected.
Thus, any specific subset of individuals (a sample) has the same chance of being selected as any other.
Sampling without replacement means that once an individual has been selected, it is removed from the population and cannot be sampled again.
Sampling *with replacement means that once the individual is selected, it is recorded as being selected, but it put back into the population. Thus, it may be selected again.
There are several reasons to sample.
You may be selecting individuals, trees, items, etc. from which to take data. Using a random number generator, or sampling from the population ensures that your data are not biased in any way.
Sampling from a known probabiilty distribution (or simulating data from a known distribution) allows you to compare your data to this known distribution.
You can sample or simulate data to test your models.