The gender gap, with respect to American government, is the difference between men and women in terms of their voting behavior. For many decades, men and women have tended to vote differently. Typically, women are much more likely than men to vote for the Democratic Party. By contrast, men are much more likely to vote for the Republican Party. An example of this can be seen in the 2012 presidential election. In that election, Barack Obama, running as a Democrat, beat Mitt Romney, running as a Republican, by 12 percentage points among women. By contrast, Romney beat Obama by 8 percentage points among men. This means there was a 20 percentage point difference in how the two sexes voted.
The main implication of this is that the parties are appealing to very different demographic groups. The other implication is that men and women apparently have very different views on politics. They may have different policy preferences. They may prefer different types of candidates. Perhaps a combination of the two causes the gap. Either way, there is clearly a major difference in voting behavior between men and women. This is the gender gap.