Both Henry and Clare experience very vivid dreams that provide glimpses into suppressed hopes and fears. Not surprisingly, they precede or follow important emotionally-charged events in their lives.
The morning of their wedding, Clare dreams that she's a mermaid. Out on the sea, she meets her mother in a sailboat. Her mother reminds her that it's her wedding today. Clare realizes that being a mermaid means she won't be able to marry Henry. She starts to cry. Upon waking, though, she decides that unlike the mermaids in Hans Christian Andersen tales, she'd be able to give up her mermaid life for becoming a regular woman without the "hideous pain in my feet or getting my tongue cut out" (B.1.14.2). It seems as though in Andersen's tales, the price for getting a different life – or, in this respect, a life with Henry – is very high, while Clare is determined that being with Henry should be relatively easy. Her attitude begs the question of whether she really knows what she's getting into by marrying Henry. Or maybe her determination is fueled by hope, rather than conviction.
The second time Clare's dream world seems to provide some insight into her psyche is when she finds herself haunted by dreams of babies. The dreams seem to reflect her pain and fears over her six miscarriages. All five dream sequences deal with disfigured babies, looking like "the small fetus of a duck," or "a gerbil with gills" – horrifying images that, sadly enough, don't stray far from Clare's true experiences of witnessing her newborns dying one after the other, because they're not quite human and not yet fit for this world, existing somewhere between life and death. It's a world that's so far away from the image of cute, healthy, smiling babies, which might otherwise be what first comes to mind when thinking about the wonder of birth. But Clare's dreams inhabit another world, a reality of fear and of alienation from what it means to be human.
Henry's most significant dreams follow the amputation of his feet. The first dream in a series of three, involves Henry putting his "lifeless, putrid" (2.26.1) feet in a box on display for students at the Newberry. His feet are disconnected from him, no longer his – a preserved but dead exhibition piece. The second dream describes Henry's experience running. Running has been Henry's life assurance, his number one weapon of escape. Running is inextricably tied to his identity as a time traveler, his sense of free will, and his feeling of some control over his life. So in his running nightmare, he doesn't seem too concerned at first when he loses his arms. He even tries to ignore that his "manhood" falls off next. But what he can't ignore is losing his feet: he falls face-first on the ground, helpless. His third and final dream pitches him on stage as the Sugar Plum Fairy in The Nutcracker. Even though Henry's feet are pumped full of morphine so he can't feel them, he knows that they're hurting. Again, it's the feeling of disconnection and loss of control over his life that Henry struggles with. The physical amputation of his feet is also the loss of his mind, his sense of self.
Birds also figure as a prominent image in The Time Traveler's Wife, providing insight into Clare's personality and her relationship with Henry. For more info, check out Clare's "Character Analysis."