The correct answer is C. Convolution of h1(t) and h2(t).
The impulse response of a linear time-invariant (LTI) system is the output of the system when the input is a unit impulse. The convolution of two functions is a mathematical operation on two functions $f$ and $g$, which produces a third function that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
In the context of LTI systems, the convolution of the impulse responses of two systems is the impulse response of the cascade of those systems. This is because the output of a cascade of two systems is the convolution of the outputs of the individual systems.
For example, if the impulse responses of two systems are $h_1(t)$ and $h_2(t)$, then the impulse response of the cascade of those systems is given by:
$$h_{12}(t) = h_1(t) * h_2(t) = \int_{-\infty}^{\infty} h_1(u) h_2(t-u) du$$
This can be seen by considering the output of the cascade of the two systems when the input is a unit impulse. The output of the first system is $h_1(t)$, and the output of the second system is $h_2(t)$. The output of the cascade is therefore the convolution of $h_1(t)$ and $h_2(t)$.
The other options are incorrect. Option A is incorrect because the product of two impulse responses is not an impulse response. Option B is incorrect because the sum of two impulse responses is not necessarily an impulse response. Option D is incorrect because the subtraction of two impulse responses is not necessarily an impulse response.