The messianic complex was a psychological condition in which the individual had a desire to redeem and save others. Some individuals were further along in the complex, having the delusion that they were a messiah saving people.
In 3189, as Michael Burnham and Cleveland Booker discussed her need to solve The Burn, she said that her brother Spock would have called her out on how she had to take responsibility for everything. In reply, Booker responded that he and Spock would have gotten on, as they both would have bonded over Burnham's endearing messianic complex. Getting in the last word, Burnham said, "Hmm. Says the man who risks his life to save helpless creatures." (DIS: "Unification III")