It's a pairing code. Your Android TV or Google TV shows it so only someone looking at the screen can connect a phone to it. Type the code from the TV into your phone app, and the phone is paired. The code can include letters, so copy it exactly.
Type the code that's on the screen right now
Pairing codes only last a short time. If pairing restarts, the TV shows a new code. Use the one on the screen now, not one from an earlier try. Google's pairing steps work the same way: choose the TV, enter the code it displays, tap Pair. Google's pairing guide
No code on the screen usually means the wrong TV is selected
If no code appears, check that the TV you picked in the app is the one in front of you. With two TVs, or a streaming box on another HDMI input, it's easy to send the request to a screen you aren't looking at.
Also check the TV is on and on the same home Wi-Fi as your phone.
In The Remote, you enter the code when you add a TV
Pick your TV in The Remote and enter the code it shows. Then the TV is saved in your list with the name and room you gave it.
After a TV update, you may be asked again
If a TV update resets the connection, The Remote may ask you to pair again. Let the update finish, turn the TV on, check it's on the same Wi-Fi, then enter the new code shown on the TV.
It's a code, not a password
You don't make it up and you don't need to remember it. There's no account behind it either: The Remote doesn't ask you to sign in.
Download the app on your Android phone (Android 8.0 or later). It works with Android TV and Google TV devices that support Android TV Remote Service v2. There's no iPhone version.