The statement that one thing is another when it clearly is not literally true. For instance, "my dog is an animal" is not a metaphor, while "my dog is a refrigerator" is. I don't know what that latter one would mean, but it's a metaphor. Metaphor is a subset of
analogy. It is different from
simile, in which one says one thing is like another.
According to George Lakoff, Mark Turner, Mark Johnson, and a bunch of other folks, metaphor is actually a basic cognitive function. They point to great deals of systematicity in our use of language which argue that we not only say that, for example, life is a journey, but reason about it in the same way. For instance, we say I'm at a dead end or I'm just getting started or I've hit a rough patch of road. All of these are metaphorical in a sense, but they don't fit the 'A is B' pattern.
However, while linguistic analysis is sufficient to show that we talk about life and journeys using the same language, it doesn't actually prove that we think about them in the same way. Sam Glucksberg argues that when we say "my job is a jail" we aren't saying that we reason about them the same way, but simply that "job" is a member of a category of which jail is a prototypical instance. How exactly he would extend this to "I feel trapped at work" isn't something he disclosed before I stopped reading about this stuff, but given how many odd machinations we have to imagine to get words out of our mouths in the first place, I don't think this one more is gonna hurt anyone.
There is some actually psychological work to support Lakoff et al's claims. The first such piece was by Dedre Gentner and her partner whose name escapes me right now, and showed that teaching people to understand electricity in terms of different metaphors led to different mistakes in their understanding of it. More recently, one Lera Boroditsky presented a cool poster at the CogSci conference a few years back that showed that people gave different answers to questions about time depending on which metaphor you used to talk to them about it. (Those metaphors would be the future is approaching us and the future is receding from us, or something like that.)
It's probably worth noting that Lakoff et al base their ideas on another idea, that of image schema, for cognitive reasoning. But I never liked image schema that much.