Upon having a taste of the yard just beyond the gate, Tilly is no longer satisfied with her small, fenced in area of green space.
She wants more.
Interpretation #1: Tilly is suffering from envy and discontent. Rather than being happy with what she has been given, she longs for what she cannot have.

Interpretation #2: Tilly is longing for a better world. She knows she lives in the confines of The Fenced in Area, but she knows there is more. She lives with the expectation that someday she will be in the Big Yard again.
What fence are you looking through? Discontent? or Longing for Something More?