This operations consists of convoluting an image A with some kernel (B), which can have any shape or size, usually a square or circle.
The kernel B has a defined anchor point, usually being the center of the kernel.
As the kernel B is scanned over the image, we compute the maximal pixel value overlapped by B and replace the image pixel in the anchor point position with that maximal value. As you can deduce, this maximizing operation causes bright regions within an image to “grow” (therefore the name dilation). Take as an example the image above. Applying dilation we can get: