Descriptive representation means having representatives in office whose demographic characteristics resemble our own. Substantive representation means having representatives in office whose policy preferences resemble our own, and/or act on our political interests. Note the "and/or" thing. It gets tricky. This can also touch on the delegate versus trustee models of representation, but mostly in this context, we take substantive representation to be based on delegate style representation, which means acting in a manner compatible with constituents' preferences.
Having people in office who look like you, whatever that means, doesn't mean having people in office who act on your policy preferences, necessarily. The issue of substantive versus descriptive representation is mostly a topic for race and representation, and in particular, redistricting, but sex too. Do women represent women better than men?
Well...
Anyway, there is a political divide at the electoral level. Since 1980, men have been more likely to vote Republican, and women Democratic, with that gap growing in 2016. Why? Your immediate answer might have something to do with abortion. You'd be dead wrong. Men's and women's opinions on abortion are statistically indistinguishable. In the American National Election Studies, we ask respondents to place themselves into one of four categories describing their opinions on abortion: abortion should never be legal, abortion should only be legal in cases of rape etc., abortion should be legal in additional unspecified circumstances demonstrating need, and abortion should always be legal. In 2016, using self-identified "gender," men placed themselves into those categories with the following percentages: 13.2%, 26.7%, 15.6%, and 44.3%. Women? 14.6%, 27%, 13.2%, 45.2%. Men and women take statistically identical positions on abortion. Why? Abortion isn't a "gender" issue. It is a religion issue. The fact that it has a differential effect on women doesn't matter if you believe that life begins at conception. So, why do men and women have different partisan preferences? Um... Uh... That's... uh...
Moving on, hey! So, how about that rape stuff?! A segue, a segue, my kingdom for a segue! Notice a few observations. First, Kellyanne Conway says that she was a victim of rape. Without qualification, I believe her. Are you surprised that she is a Trumpkin, promoting Kavanaugh? Would you expect her, a woman who has been a victim of rape, to be more supportive of the political position that sex crimes need to be taken more seriously? That would be an expectation that descriptive representation leads to substantive representation. That itself is the argument for descriptive representation. Of course, the fact that she takes money from Trump to go on camera and tell insane lies for him should tell you everything you need to know about Kellyanne Conway, and that tells you something about where the descriptive representation argument breaks down.
I made a comment the other day about politicians like Joni Ernst. The political dialog right now is focused on Lisa Murkowski and Susan Collins, but nobody is saying a word about Joni Ernst, or Shelley Moore Capito, for example. Why not? Their votes on "Brett" aren't in doubt. Of course, neither is Cory Booker's vote. Why not? Because this is about party, and to some degree, ideology. Lisa Murkowski might possibly vote no. Susan Collins, according to conventional wisdom, might vote no. Is that because they are women, or because they are "moderate?" Well, Joe Manchin might vote yes. Is that because he is a man? Um, Heidi Heitkamp might vote yes. That latter observation is very important. Heitkamp is a Democrat, and a woman. You vote for a woman, thinking you're going to get someone who stands up to a rapist, and if that woman is Heidi Heitkamp, um... not so much. Why not? The empirical problem is distinguishing between the fact that she tends to vote like a "moderate" and the fact that she represents a Republican state-- North Dakota. Is she personally moderate or does she just represent Republican constituents? That's a hard problem. Party or ideology? Hard to say, but what's easy to say is that she presents a big problem for the descriptive representation argument.
So, approach this from the perspective of a woman, who wants someone to push for strong penalties for sexual assault, etc. If you also want low taxes and minimal regulation, you may have a problem. There are legitimate arguments for those policies, and I can make them easily. I've got the econ at my fingertips. However, if you are in what Philip Converse called the "issue public" that would be associated with sexual assault, and you want someone to go hard at those who commit it, would you rather have a Joni Ernst, or a Cory Booker? Remember, I took tax policy off the table, so it doesn't matter what your opinions there are, and it doesn't matter whether or not Booker is just a showboater (which... he is). Cory Booker, or Joni Ernst, for those who want serious penalties and prosecution for sexual assault? OK, you don't like that? Would the individual in this Converse-style issue public have to vote for Cory Booker or Susan Collins? Obviously, Booker, showboater though he is. Heidi Heitkamp, or Cory Booker? You know the answer.
Does descriptive representation lead to substantive representation? That's an interesting empirical question. Don't take the answer as a given.