your questions don't seem to be related to HD wallets though!

an HD wallet is simply a wallet that is based on BIP32 proposal[1]. it allows your wallet to have a master key to generate all your addresses from. and  just like an address you have 2 sets of keys, a private one which you keep secret and a public one which you can put on your hot wallet or share.
for example a business (shoe store) creates a wallet offline and generates a master private key. then from that master private key it creates a master public key and transfers that to their cashier. there you can create the same addresses as if you had the private keys but you don't. so you are safe while you don't have to go back and forth between two computers for every address you generate.

[1] https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki