Identities are different user profiles or different users. Each identity represents a set of different data for a particular user. Data means - your email messages, folders, program settings, accounts, newsgroups, address book - everything.
While you are logged into a particular identity you see that particular set of data. When you switch identity, you see another set of data.
You can use identities to separate your data depending on how you use the program or you can use the program in multi-user environment. Some examples - if you are single user you may have one identity for work email and another for home email, you can separate your accounts by using identities, you can have 2 or more users accessing OE Classic - each one with his/hers own identity, etc.
Each user or each profile will have a different program looks when he/she enters the program. Identities can be password protected but have in mind that it is a weak protection, sufficient only against plain computer users. If you want to apply protection to your data you should use stronger protection measures (e.g. encryption).
Identities window may appear by using main menu option File » Manage Identities, or automatically when you start the program if the identity is password protected.
Top of the window shows current or active identity - the one which is logged on or the one which was logged on last time the program was running. Below is the default identity - it will be used to set current identity if there is none.
Once you switch identity, program will restart and new desktop, folders, settings and messages will appear.