In Act 3, Scene 2, Lysander uses a simile in a tirade against his former lover. He has been bewitched by a love potion and has thus abandoned Hermia for her friend. His change of affection is shocking, as it is magically induced, and when he and Hermia are reunited, he uses figurative language to communicate the extent of his disinterest. He is trying to discourage Hermia; he wants to get rid of her in order to return to his single-minded pursuit of Helena. His speech is in response to Hermia touching him. When she takes his arm, he says:
Hang off, thou cat, thou burr! Vile thing, let loose,
Or I will shake thee from me like a serpent.
In this section, Lysander uses a simile to compare Hermia to a serpent. But before he does that, he metaphorically calls her a cat and a "burr," implying that she's clinging to him (much like the prickly seeds known as "burrs," which often stick to people). He employs this language in an attempt to discourage her. In his speech, he compares her to a series of things that are tiresome in clinging to him, therefore communicating how desperately he wants her to let go of him.
The simile comparing Hermia to a serpent, though, is the most meaningful. Lysander says that he will force her to release him the way he would get rid of a serpent. His comparison to a serpent in this moment is very significant because Hermia woke up from a nightmare about a serpent as he left her sleeping side. In her nightmare, a serpent ate her heart while Lysander watched. His unknowing reference to her nightmare casts her as the serpent, implying that she is the source of poison and that, in this case, he will not hesitate to get rid of her. This statement charts as especially cruel, as Hermia’s waking wish was for Lysander’s protection from her own nightmarish serpent.
In Act 4, Scene 1, the lovers have resolved their differences and fallen happily into their proper couplings. When they are discovered by Theseus, Hippolyta and Egeus, they are tasked with explaining the situation and their feelings. As he attempts to clarify his change of heart, Demetrius uses a simile to describe his feelings and therefore clear his name. Because he is speaking to Egeus and has the task of telling the unhappy father that he no longer wishes to marry his daughter, he uses a simile to make the nature of his feelings seem beyond his control. He says:
But, my good lord, I wot not by what power
(But by some power it is) my love to Hermia,
Melted as the snow, seems to me now
As the remembrance of an idle gaud
Demetrius compares his falling out of love with Hermia to the way that the snow melts. His use of this simile makes his changing affection seem slightly mysterious and impossible to counteract. This is representative of his experience: his devotion to Hermia is undone by a magical love potion, which is administered while he is sleeping. His simile helps him communicate this sense of irreversibility and mystical power without admitting any of the details of what took place in the woods. Characterizing his love this way is to his advantage, as Egeus initially wanted him to marry Hermia. Because of his deft communication, Demetrius avoids some of the blame of not being in love with in Hermia anymore.