Do the keys that are derived from a BIP-32 HD wallet depend on an initial seed? I did not understand the concept of a seed in BIP0032 that well. Would you mind telling me do the keys that are derived from a key tree of Hierarchical Deterministic Wallet (HDW) depend on a root seed? In another words, do the derived keys differ for different root seed values or not?

Thanks in advance
Best Regards
The short answer is yes.  

A real example is provided below that applies bitcoin-explorer (bx) client on a UNIX command line interface to synthesize a very simple "low entropy" Bitcoin brain wallet seed that is 256 bits in length:

% echo “Hello its me” | bx base16-encode | bx sha256
cc64b0cb02990d2a17ba0f4274df3e38448454da4fb22a9ca8d23944be144e1d

The $seed above feeds the synthesis process of BIP 32 m/0/12d/4 private extended key below:

% echo $seed | bx hd-new | bx hd-private -i 0 | bx hd-private -d -i 12 | bx hd-private -i 4
xprv9yimFehUHrTzsGso7fg1yXqzGgAAbYJxubKbgZWzVYvf2tSNcQvbReku1xEiqmoHhhHzRsedx2a4YVQ5qf4TtkdP5DMV7dqhnK1ihKZA5Cj

Different seeds feeding the "bx hd-new" command will yield different xprv* extended private keys.

The $pvt_ext_key above can be converted into a traditional elliptic curve WIF key  below:

% echo $pvt_ext_key | bx hd-to-wif
KzWMQhXEz1Z8s5s16ArUvUEgUmX6rFahacnaMi8HMEUKFDSQ6Pks

The $pvt_ec_WIF_key above can also be directly converted into a Bitcoin address with below:

% echo $pvt_ext_key | bx hd-to-address

1ATcSQCeuQB8xNvCH7XSksNUs8SHU1dfEe