What is the wallet "word seed" that is commonly used in popular wallets clients and what does it do?
With HD wallets, a single key can be used to generate an entire tree of key pairs.  This single key serves as the "root" of the tree.  The word seed is simply a more human-readable way of expressing the key used as the root, as it can be algorithmically converted into the root private key.  Those words, in that order, will always generate the exact same key.

That single key is not replacing all other private keys, but rather is being used to generate them.  All your addresses still have different private keys...but they can all be restored by a single key.

Compare this to non-deterministic wallets.  In a non-deterministic wallet, each key is randomly generated on its own accord, and they are not seeded from a common key.  Therefore, any backups of the wallet must store each and every single private key used as an address...as well as a buffer of 100 or so future keys that may have already been given out as addresses but not recieved payments yet.

A hierarchical deterministic wallet doesn't need to back up so much data.  The private keys to every address it has ever given out can be recalculated given the root key.  That root key, in turn, can be recalculated by feeding in the word seed.

Relevant BIPS:

https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki
https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki