Your local account is the user account for your Playstation 3 system unit, and is accessed any time you use your Playstation 3 system unit whether or not you access the Playstation 3 Network. Your Playstation 3 Network account is the master account or sub account you use anytime you are on the Playstation 3 Network. If you do not want to access the Playstation 3 Network, you do not need a Playstation 3 Network account. However, you must have a user account in order to have a Playstation 3 Network account because every Playstation 3 Network account must be bound to a user account. We recommend binding your Playstation 3 Network account to your user account as soon as you create your Playstation 3 Network account to avoid cancellation of your Playstation 3 Network account.

Source: Sony