"I Am A Strange Loop" is a book that tries to support the (very plausible) idea that consciousness/soul/"I" can be largely explained by the self-aware loops of thought that we build up throughout our lives, and that no "special" essence is needed on top of the brain's universally-capable thought machinery.
This idea is part of the message of "Gödel Escher Bach", Douglas Hofstadter's famous and beautiful book in which he essentially invented the idea that the strange loops of self-reference that Kurt Gödel discovered in formal maths had deep implications for our idea of selfhood, and how that can arise from "merely" physical stuff.
Gödel Escher Bach is a masterwork, it's enchanting, illuminating, and funny. Unfortunately "I Am A Strange Loop" reads like a kind of postscript to that, a bit like someone who's not quite sure if he's got his point across so he keeps trying again and again in slightly different ways. "I Am A Strange Loop" is full of quirky analogies and lists, intended to be humourous illustrations, but one after another they quickly become very boring. Because he tries so many different analogies and doesn't stick to any of them thematically, the book seems very bitty and gets us nowhere.
If you're thinking about reading "I Am A Strange Loop", go and find Gödel Escher Bach instead - it's really a mind-altering book. If you've already read Gödel Escher Bach then read it again, and remind yourself of all the funny dialogues, the rampant thematic twists and turns and all the unexpected stuff that happens!