(The previous post on induction can be useful to read first.)
Analogy is powerful because it suggests that knowing something about one thing can help us understand something else. While Kant focussed on pairs of relationships (hand - glove; foot - shoe) Aristotle had a wider sense of analogy as an abstraction. Analogy connected to things that shared a pattern or a set of features and in doing so one could look at how one worked and gain clues about the other.
The danger of course is that while two things may look alike, they might differ in the details and even worse, in the particular details you were hoping the analogy would help you understand.
The other great power of analogy is in an even looser use - in imagining that two things are alike, we can have creative ideas inspired by one situation but useful in the other. Most often in this case the ideas are not a direct read across, but rather some kind of inspiration. But of course the health warning remains, don't imagine the analogy is reality.
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