Food is often associated with the feelings of love and sexual desire. Eating is generally seen as a pleasurable and even sensual activity, just like being in love and sexuality is also pleasurable and sensual. Since both eating and sexual activity are sensual activities, having an appetite for food is often likened with an appetite for romance, making food a common metaphor for love.
We especially see Shakespeare using food as a metaphor for love in the opening scene in Orsino's lines:
If music be the food of love, play on;
Give me excess of it, that, surfeiting,
The appetite may sicken, and so die. (I.i.1-3)
Here Orsino is likening music to the food of love, saying that music's sensuality also feeds, or encourages, sensual emotions, such as love. In calling music the "food of love," he is also likening food with love because both food and romantic desire are a form of appetite. We can have as much of an appetite or craving for romantic desire as we can have an appetite for food. What Orsino is saying in these lines is that he's hoping to fill his appetite for love so much that he becomes absolutely sick of love, just as one becomes sick after eating too much.
Hunting can also be seen as a good metaphor for love because people often become so obsessed with the objects of their desire that it is as if they hunt or stock their object of desire. In this same scene, Orsino makes a pun out of the word hart, meaning male deer, and turns the idea of hunting after hart into hunting the object of desire of his own heart, as we see in his line, "Why, so I do [go hunting after hart], the noblest that I have" (19). Orsino has given his heart to Olivia, even though she rejects it, so pursuing her is the same as pursuing his own noble heart.