The philosophy of dilation is to resize uniformly the figure in question. Under this intuitive idea, dilation is the answer. Now, what does uniformly mean here?
It means that, as can be seen in the figure, the length of every side of the right triangle can be calculated by multiplying its corresponding side in the left ("small") triangle by a constant. However, this can be done from the right triangle to the left triangle; that's why I put a bidirectional arrow.
Finally, I want to give you some motivation for this concept: Every time you are resizing an image on your phone or in your computer, you're applying this concept.