The width, in pixels, of the lines that run around the edges of a shape on the map. Generally, it makes sense to keep this value in the range of 0-10 - anything more and the lines will start to "clump" together and blot out the shape of the polygon, especially when the map is zoomed back away from the vectors.
In some cases, it can be aesthetically pleasing to completely hide the lines, and just display the "areas" of shapes on the map. To do this, just set the stroke width to 0.
To change the opacity, type directly into the input or change the value smoothly down by clicking and moving the mouse up or down on the page.