When we say their is a significant difference between two groups, we mean that the probability of seeing that difference by chance is less than or equal to 5%.
Most statistical tests rely on 3 factors to decide whether a difference is significant:
How big is the difference between the groups?
How many people or observations were sampled?
How much variation was there between the people in the groups?
Remember, statistics only tell you if there is a difference between your groups, not what caused that difference. You must rely on your study design to determine the cause of the difference.