The phrase “Brexit means Brexit” means that Brexit will take place, regardless of the implications of any other elections or political events. In particular, it means that Britain will exit the European Union even though Theresa May, who was in favor of remaining in the Union, is now Prime Minister.
After the Brexit vote, the main leaders who were in favor of Brexit have generally not done well politically. In particular, Boris Johnson was seen as a likely candidate to lead the Conservative Party and, thus, to be Prime Minister, but he was unable to gain enough support and he decided not to run. As it happened, May won the contest for leadership.
Because May had backed the Remain side in the referendum, some people had thought that she might find ways to avoid actually going through with Brexit. By saying “Brexit means Brexit,” May sought/seeks to put those ideas to rest. She wants to make it clear that she will abide by the vote and that she will initiate Britain’s exit from the EU. This is what “Brexit means Brexit” actually means.