I have an iPhone 6s and it is working as well. I am on Verizon, and my wife is on AT&T and hers is working as well. My understanding is that you must be subscribed to a visual voicemail service through your carrier (not Apple). This allows for translation of the voicemail message, although I have seen some reports that it is done locally via Siri.
For the record, I had several voicemails in my queue prior to iOS 10, and after installing iOS 10, I was able to tap on them and see the transcribed text.
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Mine either isn't working, or I haven't found it. Do I have to turn it on?
You should not have to turn anything on other than subscribing to a visual voicemail service through your carrier. To see if it is working for you, go into your voicemail messages and tap on a message. If it is activated, the message will expand and present the transcribed text of the voicemail message