If you look at tournament chips, they typically only have a number, like 100, and “no cash value” is printed there somewhere. Because they only represent tournament betting units, not actual dollars.
As opposed to cash game chips, which casinos actually refer to as cheques, because they are worth exactly what is printed on them, like $100.
In home games, some people are comfortable using cash chips for tournaments or tournament chips for cash games. But a lot of us are such sticklers for detail, that we’d never do that. For us, a $100 chip is a completely different thing than a 100 chip.
So that’s where the T comes from. And the guys above have explained how it’s used.