Understanding convolution in signal processing involves grasping the sifting property, impulse response, and the convolution operation itself. The sifting property allows extraction of a signal's value at a specific time using the delta function, but raises questions about its necessity. The impulse response characterizes a system's output when subjected to a unit impulse, leading to confusion about the nature of the delta function and its implications for system response. Convolution combines the impulse response with an input signal to determine the system's output, yet some find it perplexing why the impulse response suffices instead of directly obtaining the output for any input. Overall, clarity on these concepts is essential for a solid foundation in signals and systems.