You could have guessed that Burns wasn't addressing his poem "to a mouse" just for the heck of it—the mouse probably has some kind of symbolic meaning. But what's this little rodent doing, exactly, besides shivering in the cold after getting his nest pulled apart by a plough? Well, by the end of the poem, the speaker has discovered that he—and all of humankind—has a lot in common with the mouse.
Lines 1-2: The speaker addresses the mouse in the first line. Whenever you see a poet addressing something that can't answer back—a tree, a Grecian urn, or life, you know you're looking at an example of apostrophe. Note that the speaker uses rhyming words of more than one syllable ("beastie" and "breastie")—this is called feminine rhyme. (Head on over to the "Form and Meter" section for more on that.)
Line 4: The speaker describes the mouse's angry, argumentative chatter as "bickering brattle"—that repeated B sound is an example of alliteration, and the repeated hard consonant B almost mimics the kind of angry, frightened chatter you'd hear from a scared rodent.
Lines 9-12: The speaker draws a connection between himself and the mouse through analogy—he says that they're both born on earth and are both mortal, and so they should get along. Too bad Man has "broken nature's social union" (8), or destroyed the natural harmony between all living things.
Line 19: The speaker personifies the mouse when he describes the mouse's nest as a "housie." That personification helps to underline the analogy connecting the mouse and all human beings.