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Stratified and cluster sampling both attempt to deal with problems with simple random sampling.
The first problem is that, while a simple random sample may technically be unbiased, it may not be representative. For example, suppose my population comprises two men and two women and a sample of size two is required. Random sampling may result in a sample comprising just the two men. This may be felt to be unsatisfactory. With stratified sampling, two sub-samples would be taken (at random): one man from the two men and one woman from the two women. In this way, the proportion of male:female in the sample will exactly mirror the proportion of male:female in the population.
The second problem is that if the population is spread over a large area, collecting the sample may be very time-consuming. Suppose I wish to take a random sample of 1,000 school children across the country. It is not unlikely that my sample may require me to visit 1,000 schools. An alternative approach would be to take a random sample of 100 schools, and then take a random sample of ten school children from each of those schools. This is known as cluster sampling.
In a sense, stratified sampling and cluster sampling are opposites of each other. With stratified sampling, the population can be divided into groups (the strata) that are in some meaningful way different from each other so that, if one group were underrepresented in the sample we would regard the sample as unsatisfactory, even though it would technically be unbiased. (Note that within each stratum the population are all similar in some way: this similarity being the defining feature of each stratum. Indeed, individual population members may only belong to one stratum: there must be no overlap between strata.)
Whereas with cluster sampling, the population is divided into groups (the clusters) that are all essentially the same as each other so that, if some of these groups were missed out altogether, it wouldn't really matter. But each cluster is essentially representative of the population as a whole. (Note, again, that each member of the population should be a member of only one cluster, so that clusters do not overlap.)
Thus strata look different from each other, but their individual members are all the same in some sense. Clusters look the same as each other, but their members are as diverse as the population as a whole.
Note that the sub-sample sizes are chosen in different ways. In stratified sampling, the sub-samples from each stratum are taken proportionate to the size of the sample so that the overall sample matches the population. But in cluster sampling, the sub-samples taken from each cluster are all the same size. While this introduces a bias (members of small clusters have a higher chance of being selected than members of large clusters) this doesn't really matter.
Stratified sampling is unnecessary if the sample size is large because the sample effectively stratifies itself. If you have a population with two thousand men and two thousand women and you want a sample of a thousand people, a simple random sample will (approximately) be 50% male and 50% female. It's highly unlikely that such a sample would be very far off roughly equal proportions.
Cluster sampling cannot be avoided in the same way because the intention is different. It is designed to save resources by making the actual data collection easier.
Estimates taken from stratified samples have technical advantages over those taken from simple random samples.
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