Multiply vs Convolve: Notice that multiplying by a shifted delta yields a point sample at $t=a$, whereas convolving completely shifts the target function to $t=a$.
The Flip & Slide: Under convolution mode, watch the bottom-left panel. Observe $h(t-\tau)$ flip backward and slide through $x(\tau)$.
Adding Widths: When convolving two pulses, their non-zero widths always sum. Toggle the "Mistake" checkbox to see the common error of taking the maximum width instead.