What are the significance of gender difference in communication?
This is a very controversial topic. More importantly, your question assumes too much. The assumption is that men and women differ in their communication. This needs to be challenged and it has been for a while now. For example, most feminists say that there is no difference between men and women in terms of communication. It is true that others still insist that there is a difference. In the end, there is no conclusive proof one way or another. The best we can say is the following:
First, there is a biological and scientific evidence for differences in language between girls and boys, but it is not clear whether these differences continue into adulthood. There was an experiment done in 2008 at North Western University where 31 boys and 31 girls (from age 9-15) were tested in terms of their language abilities using functional MRIs. The tests showed that the girls had greater activity in the areas of the brain that dealt with language. But the problem with this study is that it does not project differences into adulthood.
Second, in light of this fact, it is best to say that the only reason why there seems to be a difference in communication between men and women (if there is) is due to socialization. In other words, it is society that shapes men and women to communicate in certain ways. And from observation, the difference between communication seem to be rooted more in social and economic issues than gender.
Finally, in light of all these points, the whole thesis about how men and women communicate differently needs to be questioned. More research is necessary.