When we say two sample means are different and that the difference is statistically significant, we are saying that the probability that the two means come from the same group, is so low that we can ignore that possibility and consider that the samples represent groups that are indeed distinct.

Ordinarily, one sets a standard for significance, called the alpha threshold; then calculates a p-value of the results; and last, compares the p-value to the alpha threshold. If the p-value is below alpha, the results are said to be statistically significant