“Gender is performative” means that gender is what you do, or it is produced by what you do. The word “performative” is taken from J. L. Austin’s concept of “performative utterances“, and refers to statements that are not truth propositions, but actions. For example, saying “I apologize” is not so much a statement of fact, but an action that creates the very apology it speaks of. Likewise, gendered behavior does not merely communicate who you are, but creates who you are.
“Gender is performative” does not mean that gender is acted out, as if on a stage. It does not mean that gender is pretended. Judith Butler, the originator of gender performativity theory, says so herself in this video.
Okay, but I have complaints about this video. The first thing Butler does is state the misconception, followed by “But what I mean is different.” Debunking 101: don’t do that! Generally, you should put as little emphasis on the misconception as possible, instead emphasizing the truth of the matter. People sometimes come away with a stronger memory of the misconception than of the correction. There’s a lot of literature about this, and here’s one example.
Of course, the larger issue is that Butler has already invited misconceptions with the very choice of word, “performative”. It’s just too easy to confuse “performative” with “performance”. Butler herself has used the two words interchangeably on occasion. Even when people understand the difference, they often mentally compare the two concepts, even though they have virtually nothing to do with each other.