They shed their skin basically because their skin does not grow with them, like humans.
As they grow, their skin becomes too small for them...
During a shed cycle the new skin forms underneath the old layer...an opaque fluid is released between the old layer of skin and the new one/s beneath. Which is why snakes looks blue/dull when they're in shed.
This fluid also aids shedding, providing a nice buffer, allowing the skin to slip off easily (provided the humidity level is alright)...
As you will know, the shed skin is rather brittle and crispy.
The old skin, before they've shed, is obviously too small (hence shedding)...and tight. The elasticity which helps the skin stretch isn't at its' optimum level any longer, so getting a meal down can be rather uncomfortable.
Which is why many snakes don't feed when they're in shed...the skin won't stretch as far so it can be rather uncomfortable.
Plus, whilst they're in shed, their eye sight is often impaired due to the opaque fluid under the skin...this leaves them rather vulnerable to predators. Feeding as well would make them even more vulnerable.
Having said that...a lot of snakes will feed when in shed...generally the larger species which are like dustbins anyway. And more so those that feel secure in their vivs.
EDIT: It's a bit like you wearing a really tight corset and trying to breathe!!