Here's the characteristic table for a T flip flop.
These tables are mostly here as a reminder on how D and T flip flops work, so that you don't have to flip to an older set of notes to understand the excitation tables.
I like to call the columns by the following names:
Since D = Q+, this means that we look at the column containing Q+ and copy it to the correspoding column containing D. Copying the column makes sense once you see it in the next set of notes on implementing Mealy and Moore machines.
Let's look at row 0. We have Q = 0. We want Q+ = 0. What must T be? T has two operations: when T = 0, we hold. That means Q+ = Q, i.e., the next state has the same value as the current state.
When T = 1, the T flip flop toggles the state. That means Q+ = \Q, i.e., the next state has the opposite value as the current state.
So in row 0, we want Q+ to be 0, and Q = 0, so that means we need to hold, i.e., set T = 0.
In row 1, we have Q = 0, and we want Q+ = 1. So, we need to toggle.
In row 2, we need to toggle, and row 3, we hold.
Basically, Q refers to the current state value, Q+ to the desired state value at the next positive clock edge, and the table tells us how to set D or T so that when the next positive edge occurs, Q becomes the desired Q+.
The purpose of an excitation table will be seen in the next set of notes on implementing Moore and Mealy machines.