Marching squares - reading about this for the first time. (collision with game level tiles)

I am using the http://www.java-gaming.org search to read through the collision posts. I found something called Marching squares. What I figure is that this generates a line on top of the maptiles (2d view) where the player walks on.

A wikipedia page in english on marching sqaures shows square cell grids where a line step by step is rounded around filled cells. I think I can also create game tiles that are somewhat rounded that way.

I have 'marched' player characters on graphics and learned this by programming lemmings. (look at Lemmings(mobygames/youtube)) By reading one pixel out of a image where the character is you can see if it is on or not on the map. By reading more pixels at the same time you can make the characters march vertically.