Convolution of two rectangular pulses intuition
A convolution integral is an overlap integral, i.e., for any given shift of the two aperiodic functions being convolved, the convolution integral is simply the overlap area. McGillem and Cooper [1, p. 58] defined the convolution integral of $x_1$ and $x_2$ as

$$\mathrm {x_3 =x_1*x_2 =\int_{-\infty}^{\infty}x_1(\lambda)x_2(t-\lambda)\,\mathrm d\lambda \tag{1}}$$

As a simple graphical illustration of the defining integral, they considered the following two rectangular pulses:



With $x_1$ and $x_2$ as shown in the above figure, their convolution is shown in the figure below:



This figure is redrawn from [1, p. 59]. The shaded areas are the overlap areas as a function of the shift, $t$, and the resulting convolution has a trapezoidal shape. If the rectangular pulses had had equal width, then the convolution would havec simplified to an isosceles triangular shape.

1  C.D. McGillem, G.R. Cooper, "Continuous and Discrete Signal and System Analysis", 2nd Ed., Holt, Rinehart and Winston, NY, ©1984, pp. 58-59.