statistical error
Measure the same thing ten times and you get ten slightly different numbers, scattered around the truth by jitter you cannot predict or control: electronic noise, thermal fluctuations, the luck of how many radioactive nuclei happened to decay this minute. Statistical error is that irreducible random scatter, the part of a measurement's uncertainty that changes unpredictably from trial to trial.
By definition statistical error has no consistent sign, so it averages toward zero as you accumulate data. Quantitatively it is characterized by the standard deviation of repeated measurements, and the uncertainty on the mean of N independent measurements shrinks as 1 / sqrt(N) (the standard error of the mean). For counting experiments governed by Poisson statistics, a count of N events carries a statistical uncertainty of sqrt(N), so the fractional error sqrt(N) / N = 1 / sqrt(N) steadily improves as you record more events. This slow square-root convergence is a universal fact of random sampling.
Statistical error sets how long you must run an experiment: to halve the error you must gather four times as much data. Its defining contrast is with systematic error. More data beats down statistical error but does nothing whatsoever to a systematic bias, so the two are quoted separately and treated with different tools. The classic and dangerous mistake is to report a tiny, hard-won statistical error while a larger, unnoticed systematic effect quietly dominates the true uncertainty.
Counting radioactive decays you record 100 counts in one minute; the statistical uncertainty is sqrt(100) = 10, so the rate is 100 +/- 10 per minute, a 10% uncertainty that would fall to 1% only after you had accumulated about 10000 counts.
Poisson counting: uncertainty is sqrt(N), so precision improves only as 1 / sqrt(N).
Averaging more data reduces statistical error but is powerless against systematic error; a very small statistical error can lull you into false confidence if an unnoticed systematic bias is dominating the real uncertainty.