To be in a troublesome situation that is thick with complications and difficult to get out of, hence the yogurt reference. Can refer to situations in which one is overworked, in the midst of drama, etc. Basically a euphemism for being in deep s***.
"Dude, I can't believe my girlfriend found out I have been seeing another girl on the side!"
"You're in deep yogurt, man."
"You're in deep yogurt, man."
by Xue, Tim December 5, 2008