Puck doesn't explain precisely why he changes Bottom's head into an ass's head, but he does seem to resent that the uncouth mechanicals or "homespuns" are so near his queen, saying:

What hempen homespuns have we swaggering here,

So near the cradle of the fairy queen?

What angel wakes me from my flowery bed?

Puck changes Bottom's head into an ass because he is such a poor actor. This is Shakespeare's way of poking fun at bad actors. It also leads to one of the funniest scenes in the play. When Bottom appears as an ass, the rest of his friends run away. Bottom thinks his friends are playing a trick on him, so he begins singing to show his bravery. Titania, whose eyes have just been touched by Oberon's love juice, wakes to his song. Because of the love juice, the beautiful Titania begins to swear she is in love with Bottom. Bottom replies,"''Methinks, mistress, you should have little reason for that". She then tells Bottom his is beautiful and wise. Even though Bottom knows he is not, he accepts her affection and follows her. He allows her to pet and kiss him and to put flowers on his head. Bottom tells the fairies to scratch his ears and get him honey. Both fall asleep and Oberon reverses the effect of the love juice on Titania. She wakes up and sees she has been lying next to an ass and hates what she sees. Oberon then takes turns Bottom's head into a human again. Bottom awakes and is convinced he has experienced "rare vision". He goes off to find Quince to write his vision down for him. Then he and his friends go off to perform their play, another dig at bad actors by Shakespeare.

Puck changes Bottom into a man with the head of a donkey through magic. He also uses the same magic flower intended for the human lovers on Titania, so that she falls in love with Bottom as soon as she sees him. It's appropriate because Bottom is many things, but among others, he's a fool: he is an ass. This makes his inner nature real and visible. As far as why he does it, it's because he's Puck. I'm serious. He's a creature of whimsy. He's  willing and clearly able to transform people for the sake of his own entertainment.

Puck changes Bottom's head into that of an "ass" or a donkey head.  Puck does this as a prank because he enjoys playing tricks on mortals and fairies alike.  The transformation is appropriate because Bottom's name is synonymous with "ass" and also because Bottom's personality is stubborn and pushy.  We see this when Bottom is attempting to take all the good parts of the play he and his acting group are preparing for Hippolyta's and Theseus' wedding feast.

When Bottom wakens Titania with his braying, she falls instantly in love with him.  This is a result of a spell placed on her by Oberon, the King of the Pixies.  Oberon puts this spell on Titania because they have had a disagreement, and he wishes to get revenge by making her fall in the love with the first thing she sees upon waking.  Her love affair is good for a few laughs, and then he removes the spell as she recounts the "dream" she had.