I've read a couple of pieces on how companies can raise money by building their own blockchain, and selling that blockchain's currency to customers & investors... but this interview in Fortune's term-sheet is the best explainer (okay, crypto-splainer) I have encountered!
ICOs are the equivalent of an IPO for this method of fundraising - when the blockchain's currency (tokens, coins etc.) are offered to the public. There are a few interesting advantages of this fundraising method vs traditional VC. Firstly, the everyday users are able to to participate in the value created by the service, which is nice. Secondly, currency traded on a blockchain is highly liquid, so investors aren't exposed to the duration risk typical of early-stage investments.
You could argue that equity crowdfunding also allows ordinary users (rather than just VCs) to share in the value created by their investments, but having liquidity is an awesome advantage - from an investor's perspective anyway.
Term Sheet: Bob, what is an ICO? BH: It's basically a way for blockchain startups to raise money outside the traditional VC world. TS: Only blockchain startups? BH: Indeed. It's sort of like an IPO, except for early stage blockchain projects. It's effectively a Kickstarter campaign that uses blockchain-based "tokens" (aka app coins, cryptocurrencies, digital assets) to raise money.