The whole poem is built around the device of anthropomorphism. The poem is an address, as the title states, to a mouse, as if she can understand the speaker's words to her. The speaker also attributes human traits to the mouse. First of all, the mouse is said to feel emotions like fear and "panic," "grief an' pain."
Secondly, the mouse has thoughts. The mouse doesn't just fear the speaker, she has an "ill opinion" of him. She saw the bare fields and drew the conclusion that "Winter [was] comin fast." In building her nest, she "thought to dwell" in it through the winter. The speaker claims that the mouse is affected by the "present only," while he, as a human, can look "backward" and "forward" to the past and the future. But the mouse's "foresight" in building her nest shows that she, too, shares some of this human ability to think about the future.
The speaker also takes the biblical commandment to permit gleaning, which originally applied only to humans, and extends it to the mouse. He allows the mouse her "daimen-icker in a thrave," her odd ear of corn, and says he'll find a "blessin wi' the lave," just as God promised to bless those farmers who permitted fellow humans to glean.
The speaker's anthropomorphism serves several purposes. It makes the poem more dramatic, since it turns what would otherwise be one person's solitary reflection into a scene with two characters interacting. The speaker notices that the mouse is reacting to him with fear; he must persuade her to trust him. This scene has higher stakes, too, because the speaker humanizes the mouse. If she can understand his words, then it is all the more important that he find the right words to express his sympathy.
Even more significantly, the anthropomorphism supports the speaker's claim that humans and animals share a "social union." If the mouse can think and feel in the way the speaker describes, then she has important qualities in common with human beings. These common qualities create a common bond. If humans share this common bond with animals, then they should, as the speaker implies, extend compassion towards them. Merely describing "Nature's social union" to the mouse as if she can understand the words helps show that this social union exists.