Fist of what is Minimalism defined as well as far a definition I could settle on to best explain it is hiking or backpacking with under about 10 lbs of gear. Now there is no real right or wrong way of doing minimalist type packing it all depends on what you feel comfortable packing and how much gear you would specifically feel necessary. 10 lbs may be minimal for one while 15 or 20 maybe minimal for another. If anything it makes you think about what you pack and carry on any trek or adventure, for example do I really need to carry a full backpacking cook set and such, or could you say get by with a simple canteen cup and a canteen or some similar configuration.
Another way to save weight and trim down on gear is multi purpose items, if one item can perform one or more tasks then that means thats on less thing you got to carry. Like say a metal cup like a canteen cup, or a GSI Snow peak cup. One can drink from it, cook in it, cook on it, and obviously boil and sanitize water in. The biggest item that i personally own and would use is a Guyot Designs Bottle. Its a nice stainless steel bottle you can carry water in it lid seals nice and tight; but unlike a standard Nalgene bottle you can boil your water in it. If you have the proper knowledge you can save weight by foraging and gathering food. Saves weight when you don't have to carry a ton of food.
The best way to try minimalist packing is to think of it as your emergency backup to your main pack. If you can survive a few days using at an emergency kit then adding a few odds and ends could make it reasonably possible to make due with that for a longer period of time. The biggest thing to carrying minimal gear is knowledge there is a quote in Mr. Fox's article is
"The more you know, the less you carry". The more you know how to make due with what you have and how to attain stuff from nature the less you will need to bring with you. Now again nothing is perfect there is no wrong answers here its all depends on how much you feel comfortable going into the woods with and what the requirements of your adventure require.
Finally a few pros and cons based on my personal opinions.
Less weight makes it easier on your body.
Travel faster with a lighter load.
Easier to keep balance on an awkward trail.
Less gear means little or no redundancy should something be lost or damaged.
If you find yourself in an emergency you may not have certain items that could make it easier to get out of it.
A few final thoughts think of it as a challenge where can I shave a few pounds or ounces here and there do you need this or that. Just remember have fun with it and see what you can come up with, if you already have a light weight rig you want to share feel free to post it as a comment below the blog. Take care and get out and enjoy some time out in the great outdoors.