The writer describes it as a "solution to the blockchain consensus problem that does not require mining."
The white paper is viewable here: http://tendermint.com/docs/tendermint_v04.pdf
I don't mean what are the pros and cons in relation to Bitcoin specifically, since I don't believe Bitcoin is likely to take it up. I am thinking more of the possibility of a popular altcoin like Dogecoin adopting it, or perhaps an smaller altcoin e.g. Reddcoin.