The speaker admits to something a little embarrassing: they rant. The poem opens with that blunt confession, then tries to explain or excuse it. The mouth, it says, "must have / some good Latin to flaunt," as if the ranting were really a way of showing off learning, or at least of wanting to seem learned.
The image that follows is the strangest and funniest part: "a monk in the palace / coming to look after his mind." A monk belongs in a quiet cell, not among the grandeur and noise of a court. Placing him in a palace suggests someone out of place, trying to tend his inner life in a setting that works against it. Judging by the imagery, the speaker may be describing a restless mind that goes loud in order to take care of itself.
The mood is wry and self-aware. The speaker sounds half apologetic, half amused, laughing at their own habit while hinting that something more thoughtful sits underneath the noise.