Just to follow up on alex_zag_al's sibling comment, you can have consistent estimators which are biased for any finite sample size, but are aymptotically unbiased, i.e., the bias shrinks to zero as the sample size increases without bound.

(As alex_zag_al notes, EY's explanation of bias is correct. It means that in some situations "do an analysis on all the data" is not equivalent to "do the analysis on disjoint subjects of the data and average the results" -- the former may have a smaller bias than the latter.)