What is the "hierarchical" about in Hierarchical Deterministic Wallets? So, the advantage of deterministic wallets is that you can recreate all private keys from the initial backup you created.

What's the advantage of having a hierarchy branching out from the master seed, instead of just one line of key pairs?
Hierarchy allows interesting use-cases.

You could have a master company key m/0' and give out m/0'/0/0 to company-branch A and m/0'/0/1 to company branch B, etc.

You could then allow audits by handing out the extended public keys (xpub) of m/0'/0 to some trust organization (or just hand out m/0'/0/0 if you want someone to audit branch A only).
Private key at m/0' can reconstruct all funds from all branches.

On top of that, online-shop of branch A could use the xpub of m/0'/0/0/0 to received funds while not revealing the wallet structure of m/0'/0/0, etc.

Another interesting use-case would be to map domain-names or other string-based- identity-systems to the hierarchy. Example: Github.com could result in m/71'/105'/116'/104'/117'/98'/... (very unoptimized way for demonstration purpose).