Consider the phrase: "wrestle with a dilemma." What does this phrase mean; what figure of speech is it?

To wrestle with a dilemma means to have difficulty deciding between competing resolutions of a problem. This phrase is an example of personification, in that the activity of deciding between alternatives is likened to the activity of wrestling. So the dilemma itself is talked about as if it is able actively resist solution, to fight back, as it were, against being pinned down.