As with many of the other figures discussed in this series, personification and apostrophe are technical terms for linguistic phenomena that we use unconsciously in everyday life, not complex devices employed only by master poets. The root of the word personification gives us an important clue as to the meaning of both of these terms, and if you think about it carefully, you can almost derive the definition of that term from simply reading it. PERSONification employs the word person, and ends with a relatively common suffix that is employed to make a verb into a noun. Personification is therefore the act of treating something that is not a person as if it were; sort of.
Technically, this definition is somewhat too narrow, though it is a helpful way to remember what the term means in a general way. More specifically, personification is the treatment of inanimate objects, non-living things, and abstract entities as if they were living things. Note how his differs from the preliminary definition above; you don't need to treat something as a person necessarily, just as a living thing. A classic device of the fable, treating animals as if they were human, is called anthropomorphism, which resembles personification, but which must attribute human characteristics to any non-human being.
An obvious illustrative example of personification rests in a common poetic image:
"The leaves danced in the cool breeze."
Immediately, we know what is going on here in a literal sense; the leaves are being blown around by the wind. However, notice how much more satisfying and evocative this personification is. First, it attributes the agency to the thing being described, which makes the leaves spring to the foreground and come to life. Next, it makes the movements of the leaves more specific, allowing us to visualize them flitting about in a somewhat rhythmic and gentle fashion instead of being blown wildly about. Finally, it sets the mood of the scene efficiently, since dancing is a happy, joyous activity in general.
This brings us to a specific kind of personification, called apostrophe, which refers to a direct address to an inanimate or abstract entity as if it were a human capable of understanding the address. One of the most famous examples of this phenomenon is "Death be not proud" by John Donne, where the speaker addresses death throughout the poem, cautioning him/her not to be proud, for in the end death is defeated by eternal life. This device is sometimes made even more apparent by capitalizing the entity that is being addressed, making what is often an abstract noun (like death) a proper noun or a proper name, as Chaucer does in the Canterbury Tales, again with Death.
The effect of this device shares some characteristics with personification, but most often has an even more profound impact because the personification is extended and developed in a more detailed manner. In the case of Donne's poem, by using apostrophe the poet is able to express an emotion which often accompanies the death of a loved one, anger, but rather than address it to a particular individual or even God, which are both common targets, Donne turns his anger against its true cause, death itself. As a result, the expression of his emotion is pure, and he makes it so all of us who have ever lost someone can relate. He targets a universal phenomenon all of us have experienced to some degree rather than any specific individual, making the poem personal for all who read it.