Let's take the example of the number of people who walk into a store and buy a certain product. By studying 10 customers you can get an estimate of the probability of the purchase and predict sales; by studying 100 customers you get a better estimate. By analyzing 1000 customers you have a very good estimate. You could study a million customers, but the results are unlikely to be vastly different from the results of analyzing 1000 customers and probably not worth the expense.
This makes sense only for very low-dimensional data sets, but most real-life problems are very high-dimensional and in high-dimensional spaces a million customers (or any other number of samples you might reasonably expect to gather) might still very well be only a small sample. So, there are situations where because of various constraints you will never be able to get to this level where more data stops yielding better results. You can watch a nice presentation from Peter Norvig about the unreasonable effectiveness of data:
http://www.youtube.com/watch?v=yvDCzhbjYWs
Or read about the well-known curse of dimensionality: