Its the range of analyte concentration that gives a "linear response". For example, your concentration is 1M and your output (peak area) is 1, then your concentration is 2M and your output is 2, 3M = 3 and so forth. This is linear response. Eventually you will get to the point where , say, your concentration is 4M and your output is only 3.5. Now you have gone out of linear range. This is just a crude example to illustrate the point.