Personification is giving human characteristics to non-human things.
In Act One, scene one of Shakespeare's King Lear, the first example of personification can be found in line 115, where the heart is personified.
Here I disclaim all my paternal care,
Propinquity, and property of blood,
And as a stranger to my heart and me
Hold thee from this for ever.
Here the heart is personified as something that is not an organ beating in one's chest, but a being in itself. And that Cordelia's words and sentiments make her a stranger to his heart—and himself. (Lear indicates that he and his heart are like separate entities.)
Again we see personification in line 150.
Think’st thou that duty shall have dread to speak
When power to flattery bows?
In this segment, power and flattery are both personified as Kent questions Lear's wisdom in exiling Cordelia and cutting her off from her inheritance. People bow, but "power" and "flattery" are inanimate, non-human things to which human characteristics have been given here. "Power" cannot bow to "flattery."
In lines 264-265, "love" is personified:
Tis strange that from their cold’st neglect
My love should kindle to inflamed respect.
Here the King of France tells Cordelia that his love has changed, grown in its capacity to respect her, even though she is now the discarded daughter from her father's kingdom. "Love" is something we do. We can speak of loving someone or something. But when we speak of "love" in terms of it "being" something, such as shy, guarded, forgiving or "respectful" (as is the case here), we personify it. Love cannot have human characteristics. We often describe love in such terms and in doing so, personify our love.
Why, then, does Shakespeare use personification in this play? There can be many reasons. First and foremost, figurative language that uses words not to be taken literally is powerful in the way in which it touches the reader—and in a play, its audience. Personification is not meant to be taken literally, but gives the situations being described a deeper meaning and a more forceful impact. This is one main of the tools of writers—the use of figurative language.
The second reason Shakespeare may also use personification is to play games with words because Cordelia's lack of the appropriate words to her father are her downfall. Honesty and words spoken literally are not what Lear wants to hear. He wants Cordelia to praise him, regardless of whether the words are empty or not. Whereas her sisters praise their father for what it will get them as he divides his kingdom, Cordelia speaks with love and respect, but not in flowery terms. Personification makes for more "flowery" speech, and I would surmise that Shakespeare is making a point about how language can change, and change things, but that words can be misleading. Lear is misled by his older daughters, but resents that Cordelia will not play "the word game" as Goneril and Regan have done.