Besides from being a namedrop for the album, Jay and ‘Ye are saying they have armor to protect themselves.
It also sums up the theme of the album — hip hop is currently on music’s ‘throne’ where rock used to be, and Jay and Kanye are at the pinnacle of that, but if they do watch the throne and continue to push themselves, one day somebody else may steal it. He might also be saying that he has body armor because “a nigga gotta watch the throne”, i.e. The Throne (aka the rich/ upper class) is a place where he is now, thus making him a high priority target for others trying to steal his fame.
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