To some extent, the defining theme of "third-wave feminism" is that there is no one single defining theme. That makes a lot of sense. Just like Enlightenment ideas went from a set of pretty narrowly focused concepts espoused by a small group of people who were socially and geographically proximate to widely-established and accepted ideas being developed in a host of ways (from anarchism and socialism to classical market liberalism to utopian communities to a growing belief in science per se as a way of driving forward the species which we today see in transhumanism), so too did feminism go from very geographically limited and socially proximate movements with definable leadership to an array of causes and movements.
Feminism during this period became entangled with LGBTQ concerns. Obviously lesbians had to be part of the sisterhood, and obviously patriarchal messages harmed all LGBTQ minorities by establishing a strict gender and attraction binary.
Feminism began to become involved with and affected by decolonization and post-colonialism as well as anti-racism and civil rights. A range of Third World feminisms
Because feminism now had over a century of academic development and real heavy-hitters like de Beauvoir in major philosophical circles, feminism during this time also became more academic. To me, this may be one of the major weaknesses of third wave feminism: An ivory tower retreat is always easier than the tough work of real activism.
What I think characterizes all of the third-wave feminist movements, though, is a growing, broader recognition of what oppression is. The first and second waves focused on issues that are directly and obviously institutional or about expanding options. It's relatively easy to say, "It is not just for women to vote" or "It is not just for women to be paid less" or "It is not just for women to not be represented equally in the legislature" or "It is not just for women to not have practical options to not be married and to be out of home". Just talking about giving people more choices and creating measurable equality is relatively uncontroversial.
Third-wave feminism began to recognize that some "options" are so tainted by patriarchy and other forms of oppression that they should be heavily limited. What options those are is obviously up for debate, but a few one might discuss might be a traditional male-dominated marriage, BDSM-based relationships, and pornography. In each case, someone might say, "Look, this is my right and my choice", and a feminist might say, "That choice is one you've made due to the way that patriarchy gives you incentives to use your body as currency and to be demure and submissive. You have a desire to be that way because society told you that that was the good way to be and because of the blinders of nostalgia, but it's actually destructive to human potentials". That's where some of the biggest debates are. Well-meaning people will differ markedly on the range of behavior that is healthy for human beings.
Similarly, third-wave feminists have focused a lot on cultural artifacts: Video games, books, movies. This is a tough area to focus on because there is a large amount of subjectivity there, but at the same time it just seems so clear to anyone thinking carefully that there is no reason that the top movie franchises in the world are all overwhelmingly male-dominated. Think for a second about Marvel and Star Wars. Star Wars finally has a female protagonist with The Force Awakens, but she is definitely in an ensemble in that film. Contrast that with the clear protagonist focus on Luke in the original three films and Anakin (and Obi-Wan) in the prequel films. When it comes to Marvel, while Black Widow and Scarlet Witch are Avengers, every one of the current films (as of January 2016) is headlined by a male protagonist: The one canon Hulk film, all three Iron Man films, the two Captain America films, the Ant-Man film and the two Thor films. In the TV canon, Agents of SHIELD is an ensemble show with multiple strong female characters (but arguably with the protagonist duties split between Skye and Coulson), Agent Carter has a female protagonist, and Daredevil and Jessica Jones split down the middle. The TV canon on its own would actually be a gender-progressive array, if it weren't for the context of the big money makers in the films.
One could argue that it is somewhat silly to be focusing on these more subjective aspects of inequality or oppression while major problems like FGM, inadequate policing of rape, the gender wage gap, underrepresentation of women in the top echelons of industry and politics, etc. is still routine globally (even as major victories have certainly been won). But I would argue, in defense of third wave feminism, that it is precisely the more subjective aspects of inequality and oppression, the more emotive and personal, that restrict us so heavily in visceral ways and make the easier-to-trace inequalities possible. The fact that our stories so often lionize males, even when written by females (like Harry Potter lionizing a male protagonist despite being written by a female), helps to give boys heroic role models to look up while limiting how girls can imagine themselves as strong, capable and fully-fledged people. The fact that we have subconscious biases about the competence of women and the fact that we have social network biases against women helps to keep women out of the highest echelons. The fact that we have the second shift at home heavily constrains the options for women to achieve equality in the market or in politics, which in turn helps to legitimate oppression by making it look like women are "choosing" to make less money.
To some extent, then, feminism in the third-wave is based on the idea that "the personal is political" (which, as Michael Albert has argued, should not be confused for "the political is personal"). The enduring power of that slogan, whatever its flaws in practice, can be viewed as the center of third-wave feminism. And whatever one thinks of third-wave feminism, certainly more women than ever before in history are expressing themselves in the academy and in society as a result.