The edge based subdivide core looks at each selected edge and performs the specified number of cuts on that edge. Then, each face is examined for cut edges and is filled with the appropriate pattern, based on how many edges were cut and whether the face was a tri or quad.
There are 8 basic cut types. Here they are shown in each column, with cut numbers from 1 to 4.
This is the workflow for new loopcut tool
When an edgeloop is selected, pressing X (delete) brings up a menu. Choose "Edge Loop" from this menu to remove the edgeloop and merge the surrounding loops.
The updated subdivied tools also include support for edge ring selection. Select an edge ring by clicking with CTRL-ALT-RMB on an edge. Using edge based subdivide on an edge ring is the same as making a loopcut.
Slide a selected edge or edgeloop along its perpendicular edges. Technically, this is not related to subdivide, but will be very handy in conjuction with the Loopcut tool. Activiated by selecting an edge or edgeloop and pressing CTRL-E, then choosing EdgeSlide from the menu.
The knife tool has been updated to work with the new subdivide code, allowing for cleaner cuts and the ability to do make multiple cuts with one action. Select the edges to be cut and press K-KEY to access the menu for the knife tool.
See this wiki page for information about bugs and the future direction of these tools: