Text log is an interface item / widget that you can use to display some text. When it receives new text, the old text will automatically scroll up, like in a computer terminal. The text log is intended mainly for debugging purpose. For example if you are developing a gadget and you need to output some debug info at specific parts of your code, then simply send it via UART and have your device connected to RoboRemo. The debug info will appear in the text log. You can add a prefix to the string you are sending and also set the id of the text log to that prefix, so you can have different strings appear in different text logs. See the video below for a text log example.
And here is the Arduino code: