You can extract your master public key from electrum via:
This will output a 128 character hex string that is used as the seed for all the *public* keys in that particular wallet
Revealing your master public key has an impact on your anonynimity. Anyone with that master public key can determine the set of addresses that are associated with that wallet.
This page uses the Deterministic Bitcoin Address Generator (prusnak/addrgen) for the address generation.
It also uses blockchain.info to see which addresses have transaction on them already to avoid used ones.
The max look ahead is 5 addresses, matching the Electrum default gap limit.