"What is 'muscle glycogen'?"

Glycogen stored in muscle. For LCers, this is "good" glycogen, compared to liver glycogen which effects hormone levels relating to ketosis and fat metabolism.

"How is it different from glycogen in general?"

It's not. It's the same type of glycogen as liver glycogen, for example, just stored in muscles. Once in the muscle, though, it can only be used for muscle activity, unlike livery glycogen which can be released back into the bloodstream for use elsewhere.

The term "partitioning" is common among body builders, it means deciding where nutrients go inside the body. Mostly, it's genetic - a certain percent goes to muscle, a certain percent goes to fat stores, a certain percent goes to metabolism, etc. Changing partitioning is a common pursuit, using techniques ranging from exercise and diet to prescription performance drugs.

"Why would muscles be more sensitive to insulin than the rest of your body?"

Mostly that's genetic - each component of your body (it even varies between muscles) has a certain sensitivity threshold. Most of the effort "we" put into insulin sensitivity is to move the balance point as much as we can towards muscle and away from fat.

There are a few factors that can influence partitioning by changing insulin sensitivity for muscles, fat, and liver in different (i.e. unequal) ways. Just the fact that muscle glycogen stores are low will make muscles more insulin sensitive. That's why long-term LCers will "bloat" by many pounds if they eat carbs - most of it goes to muscle stores, and the water required to store it can add 5-10 lbs very quickly. Liver storage alone can only account for about 1 lb.

Exercise can also make muscles more sensitive, both by depleting glycogen stores even more, and by enzyme changes due to the exercise itself causing cell stress (i.e. strength training does this more than cardio).

Fish oil is a common dietary aid that increases muscle sensitivity and reduces fat cell sensitivity. Various performance drugs also do this, but with much more "interesting" side effects.

So, in a cyclic diet, you commonly two two phases: First, you LC and low calorie diet, while doing high-rep medium-weight workouts to fully deplete muscle glycogen, and stay there for a few days to really boost insulin sensitivity. Then, one more workout to get the enzymes going so muscles are REALLY sensitive and the liver is way into ketosis, then WHAM eat a big load of carbs and the muscles just suck them up so fast the liver and fat cells don't have time to react.

For more information, google for "Cyclic Ketogenic Diet", "BodyOpus", or "Ultimate Diet 2.0", or see http://www.bodyrecomposition.com/ for the "The Ketogenic Diet" and "Ultimate Diet 2.0" books.