E-Tray exercises test your time management, prioritisation, written communication, and analytical skills.
Typically, you will be given a simulated inbox containing emails and asked to prioritise and respond to them. As you undertake the test, you will receive more emails.
Alternatively, you may get a series of documents; memos, letters, emails, and reports. Your task will be to respond according to the instructions.
The Wiki job forum is a good source of information on the exercises used by different companies.
You can practice E-Tray exercises on Graduates First.