'This makes no sense!' Alice proclaimed.
With a sigh, the caterpillar stopped smoking. 'You are here.' He pointed at the circle. 'You want to get here.' He pointed to the line leading away.
'But what are all these numbers?'
The caterpillar grumbled. 'On top of each hedge (each white square) is a jubjub bird. Now some of these jubjub birds are angry, and are on the lookout for prey (the arrows tell you which directions the angry ones are looking). If a jubjub bird does not see you pass through paths in the directions they are looking EXACTLY the number of times specified, they will gobble you up before you can leave the maze!'
'So, to make sure I understand, I can't pass through the path right above the jubjub bird marked zero? And I will pass through seven paths in the same row or column as the jubjub bird marked seven?'
'Sounds good... just don't reach the same intersection more than once...' He put the pipe back into his mouth, and Alice knew it was up to her to get out now.
EDIT: The rightmost five should be looking LEFT RIGHT and DOWN, not left right and up. I'll make an edit to the image when I get home.