Since it is the current wave of feminism that is being mobilized as I write this, it's hard to argue that fourth-wave feminism is not clearly the most relevant today. In the past, feminism focused merely on the social mobility and liberation of women; though these were important steps to take, fourth-wave feminism is far more inclusive of all sorts of marginalized groups.
One of the most important aspects of fourth-wave feminism is the adamant inclusion of the rights of transgender people. Several waves of feminism in the past had the unfortunate tendency to be trans-exclusionary. In the 2010s, a huge contingent of trans and genderqueer people have made themselves more visible, and understanding, valuing, and fighting against the marginalization of this population is one of the core tenants of fourth-wave feminism.
Furthermore, fourth-wave feminism is largely focused on disrupting the patriarchy in the workplace, focusing intensely on the "boys' club" fashion in which business has previously been conducted. Fighting back against harassment and disproportionate opportunity is a major goal.
Finally, fourth-wave feminism puts an enormous emphasis on class struggle and on marginalized groups beyond just women. This brand of feminism recognizes that the patriarchy is, sometimes unwittingly, responsibly for many different social problems. Fourth-wave feminists are not exaggerating when they claim that "men need feminism too." Indeed, fourth-wave feminism identifies a power structure that is predominately white, male, straight, cisgender, and upper class, and attempts to disrupt it through activism ranging from representation in business and politics to social media.