A Significant Difference between two groups or two points in time means that there is a measurable difference between the groups and that, statistically, the probability of obtaining that difference by chance is very small (usually less than 5%). Thus, it is safe to assume that the difference is due to the experimental manipulation or treatment.
Statistical difference should not be confused with the size of the difference between the groups. One group may have a mean score of 95 while another has a mean score of 98, and this result may be statistically significant but not a very large or meaningful effect.