In The Odyssey, one epithet is "when rosy fingered dawn appeared." What type of figure of speech is this?
Consider what this expression does to dawn. What is the expression "rosy fingered dawn" giving to dawn? Hopefully you should be thinking that it is giving it human characteristics, by referring to the "fingers" of dawn. Thus we can say that this figure of speech is an example of personification. Of course, in the Greek world vision, Dawn in a sense was personfied anyway as a Goddess who brought morning into being, so perhaps this helps us to understand the way that dawn is personfied throughout this great epic classic.
However, just to remind you, personification is a figure of speech where an inanimate object is given human characteristics, in either actions or appearance. Note how the "rosy fingers" perhaps refer to the effect on the sky as the sun rises and how beautiful patterns appear.
It is already appropriate enough to describe this phrase as an epithet, of the sort with which the Homeric verses are rich. However, we might also call it a descriptive phrase. As it applies human attributes to aspects of nature, we could also say that it is an example of pathetic fallacy.
Pathetic fallacy is a conceit in which natural elements are afforded human motivations and attributes and are described as if they are human. In this instance, dawn is described as being human in that it has rosy fingers, whereas in actuality, this is only a figure of speech. We could also interpret this as a metaphor, where the clouds spreading across the early morning sky, limned in pink and gold, are represented as the fingers of dawn.