I've been using a pretty old version of Multibit classic and recently decided to upgrade. I tried out Multibit HD and Electrum and noticed that both have me set up a wallet with a "word seed". It's just a string of random words that is apparently used in an algorithm. The question is, what does it do exactly? Someone told me that it generates private keys for you, and all you need is that word seed and you will be able to restore/generate all your private keys. How does this work exactly? What algorithm is being use on the seed to generate the keys?

These words are apparently very important, as Multibit warns on their site:

To restore your wallet and recover your bitcoin, you must have your wallet words.

With your wallet words, you can recover your bitcoin. You must keep your wallet words safe, because anyone who knows your wallet words can steal your bitcoin.

The seed words seem to be a replacement for the private keys, based on what Multibit says about them. I'm personally quite attached to the idea of having my private keys, so why should I be content with this word seed instead? Some apparently think it's safe enough: Is 12-word seed phrase safe enough?, but is it usable enough?