Most people who found themselves up a tree with a bee would feel alarm, or at least irritation. Lear's Old Man feels boredom, and that one word choice carries the whole joke. "Horribly bored by a bee" sets a dramatic adverb beside a limp, yawning verb, so the bee, which ought to be a threat, becomes a tedious companion, like a dinner guest who won't stop droning on. The poem is about a tiny grievance blown up to heroic size, and its central idea is that nonsense works by getting proportions slightly, delightfully wrong.
The comedy deepens when other voices arrive. "They said" is all we are told. We never learn who "they" are, how they came to be chatting with a man in a tree, or why they ask. Their question, "Does it buzz?", answers itself, as if buzzing were a surprising habit in a bee. The Old Man replies with wounded energy: "Yes, it does!" The exclamation mark turns a plain fact into a scandal. Then comes the verdict: "a regular brute of a bee." "Regular" here has the old sense of thorough, out-and-out, and "brute" is a word for a bully or a beast, far too large for an insect. Stripped down, his complaint is that the bee behaves exactly like a bee, and he treats this as an outrage.
The form sharpens the joke. This is a limerick, rhymed AABBA, and the rhythm bounces in the way limericks do: *there WAS an old MAN in a TREE*, with two light syllables tucked between each beat. That lilt makes the poem sound like a nursery rhyme before we have taken in how odd it is. The two shorter middle lines, "When they said 'Does it buzz?' / He replied 'Yes, it does!'", have only two beats each, so the exchange feels like a quick back-and-forth, and the longer final line then unrolls for the punchline. Even the rhyme in those lines is a small pleasure, since "buzz" and "does" are spelled differently but sound the same.
The ending is where the construction gets cleverest. Instead of finding a fresh rhyme for the last line, the poem repeats "bee", the same word that closed line two. So the poem circles back to where it started, and the man is no further forward. He is still in the tree, still with the bee, still bored. The lack of progress is part of the humour, because nothing happens, nobody helps, and no explanation arrives. There is no moral and no rescue.
Sound does quiet work too. The poem is full of b's: *bored*, *bee*, *buzz*, *brute*, *bee*. Said aloud, they make a faint drone, as if the bee were humming under the words. "Buzz" itself is onomatopoeic and falls on a stressed beat, so the sound of the bee appears in the very line that asks about it. Imagery is otherwise spare, with only a tree and a bee. We are not told what the man looks like, how big the bee is, or why he climbed up there. The capital letters of "Old Man" make him a type rather than a person, a figure from a tall tale, and the gaps invite us to fill in the picture ourselves.
That economy is much of what makes the poem significant. Lear is remembered as a leading name in nonsense verse and in popularising the limerick, and this small example shows why the form suited him. Five short lines are enough for a character, a situation, a bit of dialogue and a punchline. Nonsense here is not randomness. The logic is almost normal, which is why it is funny: a man really is annoyed by a bee, but his reaction is absurdly mismatched to the cause. Behind the silliness is something recognisable too. Everyone has been exasperated by something that cannot help being exactly what it is, and the Old Man's solemn outrage at a buzzing bee lets us laugh at that feeling.