Until about the 1970's in academia, and the 2010's for the general population, the word gender was used interchangeably with the word sex. Gender was often used in communication rather than the word sex, to eliminate any confusion of "sex" referring to sexual intercourse.
Instead, confusion now arises because "identity" is conflated with "gender" in mainstream usage. Basically speaking, gender theory is the concept that while a person may be biologically female or biologically male, she or he has the right to identify herself or himself as female, male, both or neither.
This idea is increasingly taking hold in academia, politics and society, and can be easily understood to be detrimental to the interests of women. What looks at first glance like "freedom of choice" is perhaps under the surface actually just a heinous and convenient tool to undermine and reverse the momentum, gained over decades of struggle, in the improvement of life quality women have achieved through the women's liberation movement.
Without elaborating in detail, Pope Francis addressed the gender debate using the phrase "ideological colonialization". This is a perfect description for many societal processes that are occurring right now at an unprecedentedly rapid pace, changes that are primarily triggered by technological advancements being used to subvert democracy as we know it and advance technocratic hegemony. The "gender debate" is just one piece of the puzzle in the current reorganization of society.