Grow or shrink the bright parts of a picture. Dilate takes the brightest pixel in a neighbourhood, so light regions swell into dark ones. Erode takes the darkest and does the reverse.
On a mask these thicken or thin it, which is the everyday use: closing small gaps, or nibbling a selection back from its edge. On a photograph they give the waxy, melted look of the classic minimum and maximum filters.
shape is worth knowing about because it changes the cost as much as the result. A square neighbourhood can be done in two cheap passes, one across and one down, because the brightest pixel in a square is the brightest of each row's brightest. A disc has no such shortcut and has to be checked in full, which is hundreds of samples per pixel. Round looks better on curves; square is much faster.