Asymptotic Error bound

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Asymptotic error bound is the limit on the error when the size of sample goes to infinity. Am I right about this? If not can somebody explain what Asymptotic error bound is? And the situations in which we can use them?

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Asymptotic error bound generally refers to the expected amount of error in some estimate as some other number goes to infinity. In statistics, the context is often that standard error tends towards zero as the sample size tends towards infinity. Or alternative it could be a reference to the fact that standard error is related to the squarer root of the sample size. So standard error is less than or equal to sigma/sqrt(n), where sigma is standard deviation and n is the size of a sampling distribution.