C

To understand what the area under the acceleration-time graph represents, we first need to recall the definition of acceleration.
Step 1: Acceleration is the rate of change of velocity with respect to time. Mathematically, this is represented as:
$$ a = \frac{dv}{dt} $$
Step 2: When we plot acceleration on the y-axis and time on the x-axis, the area under the acceleration-time graph over a specific time interval gives us the change in velocity. This is due to the fundamental theorem of calculus, which states that the integral (area) of a function gives us the total change of that function over the specified interval.
Thus, if we calculate the area under the graph from time $t_1$ to $t_2$, we can express it as:
$$ \Delta v = \int_{t_1}^{t_2} a \, dt $$
Step 3: Therefore, the area corresponds to the change in velocity (final velocity - initial velocity) over that time interval. Hence, the correct answer is option C: Change in velocity.