A bias of a measurement or a sampling procedure may pose a more serious problem for a researcher than random errors because it cannot be reduced by simply increasing the sample size.
For example, if electronic scales systematically increase the real weight by, say 0.1% (besides the random variation in both directions from the true weight), then the averaging over 1,000 or 1,000,000 measurements still has the same bias – 0.1% higher than the true weight.
Another example is an opinion poll focused on presidential candidate preferences among the population of New York City. A random sample of 1000 individuals has been drawn at random from households in the borough of Queens. If personal preferences vary from borough to borough within NYC, then such a poll is biased. Even if we increase the sample size up to 100,000, the systematic error is still the same. (The bias is equal to the difference between the population of this region and the whole city population.)