To understand, mostly. Something you say when you think you've almost got it, almost understand.
After being told to remember a long list of directions to get to the airport, she said, "I underconstumble".
It basically only means understand. Its a way to make yourself sound like a 6 year old.
"Dude: Hey, sorry I couldn't go for a walk with you today. Mom wanted me to go to town."
"Dudette: Yeah its all right, I underconstumble."
"Dude: what are you, six?"