Picture yourself moving a loaded 55 gallon drum across your shop, or whatever, floor. This is basically how you "walk" the cup. You don't pick up the drum, you roll it side to side, to move it across the room. Hope this helps.

Walking the cup is a term related to TIG welding whereas any good TIG welder will use. It is a term describing using a cup sized for the groove. You would then place the cup directly on the bevels and weave. This provides stability for the root, hot pass and any filler passes where you can get the cup into the groove. Of course you would have to change cup sizes for each pass, then freehand the final passes. It also helps when the welder has a hangover and can’t hold his hand still (just kidding. We know welders don’t drink). Slagman's description above regarding the 55 gallon drum is pretty much a good description. I hope that answers your question. If you use that Down Under and have a term for it, please tell us what it is.

My first experiences with "cup-walking" ocurred with the influx of out-of-state welders to central Michigan in the late 60's for a nuc plant being built across the river from my chemical plant.
What Slagman and NDTIII have said is correct but I'd like to try and expound on it a little further from my experiences with steel, SS, & nickel alloys in schedule 10 thru 80 in NPS's to 6".

It has been my experience to use no land but rather a sharp edge to the bevel. The root opening should match the diameter of the filler rod because you will be drawing off the rod continuiously (no dipping & no keyhole). Similar to "free-handing" your torch angle will govern the depth of root penetration but you will start with a greater torch angle (45 degrees, some more some less) most welders opt for a torch with a flexible neck. With SS and carbon steel visual indicators affecting the molten puddle (similar to "free-hand") will allow you to verify fusion & penetration (dancing star, center fusion line, puddle sinking, etc.) Amps will be considerable lower then when "free-handing" which is a serious plus over SS "free-hand". In most cases your torch and your arm will be quite inline with the joint instead of askew and where your arm goes so goes the body, it will face more in line with the joint. Because of the wrist manipulations starting with a wiggle during the root application (just catching the edges) to a broader stroke, rolling type weave during capping most welders find it less tiring and adds balance to the arm if you have a couple of wraps of torch lead around it. Most welders will jump one cup size for capping.

Given all things equal, SS and carbon steel tack tie-ins and the backside root bead surface will be noticable smoother then with "free-hand". Infact, this is one of the first things a welder notices with this technique is how smooth his root looks inside second being how much narrower his heat-affected zone is.

The "cup-walking" technique is ideal for shop and many field applications where joints are relatively uniform and positioning of the joint allows access for the technique to be used. But there are still plenty of times out in the plants when the "free-hand" technique is a necessity to use.

It's been my experience that nickel alloys (Inconels, hasteloys, monel, etc.) are very difficult to apply a root bead (open root) with the "cup-walking" technique. Nickel alloy puddles don't appreciably exhibit visual indcators of fusion or penetration. Most of the welders I find using the technique on nickel alloy root beads, program themselves to a travel speed with amps that they have had success with (repeditive joints). The problem quickly becomes apparent when they are required to weld a base metal of a different thickness. Fill and cap passes are no problem with the technique though.
Please understand these are only my experiences and welding experiences are as varied as there are the number of welders!
Give it a try and if you are carefull not to bear too hard on the torch, you'll enjoy it. As a welder becomes more proficent with it, his boss will think he has a machine because of the uniformity.