Okay I am assuming you know what vertices or vertex (points where the edges come together and join) are.

Using your thumbnail image above i will attempt to explain each image from left to right . First off you need to know that the smoothing is done from one vertex point to next nearest vertex point, so the closer the points are to each other the tighter the curve or radius will be.

So from left to right the first image has equal sides and equal distance between points so when smoothed it curves equally in all directions making a sphere or ball.

The second image has a split or edge loop very close to the right side so because the vertices on the right side are so close to each other the radius of the curve is very small so it holds the shape of the edge and only smoothes in the very corners between the two close edges, the other side is free to smoothe the etire distance of the egde or vertex to vertex so it curves the same as a ball or sphere just like the first image.

The 3rd or center image has a split or edge loop in the middle of the cube so that line creates hald the distance between vertex points on that side so the radius is shortened above and below the loop because there is another vertex added when creating the edge loop, so you end up with almost a circle at the top and bottom where there i no loop and the center where there is a loop becomes straighter because the edge stops it from curving.
Th next image is the sme thing as the last but vertical instead of horizontal,creating the same shape just rotated 90 degrees.

The last image on the right is just like the second image on the left except it has a close loop on the left and right sides so both the left and right edges are held by the radius of the curve being very small so only the sides without the edge loops curve fully from edge to edge giving you the cylinder shape.

I hope this is clear to you as English is not your first language and i really hope it helps a little in your understanding of smooth in Maya.