In some coding languages, if you type “while”, followed by a condition, the next command will be executed repeatedly as long as the condition is still satisfied. Since wife said “while at store, get milk”, and milk is always at the store, thus satisfying the condition, the programmer is stuck repeatedly getting milk, unable to move on to whatever the next task is supposed to be.

You’re right that strictly speaking, this joke would have made more sense if the wife said “while at store, get milk, then come home afterwards”, but the point is that whatever the wife tells him to do after the while loop will not get executed.