state function
Think of your altitude on a mountain. Whether you reached a given spot by a gentle winding trail or a brutal vertical scramble, your height above sea level is the same — it depends only on where you are now, not on how you got there. A state function is any property of a system that behaves like that altitude: it depends only on the present condition of the system.
Formally, a state function is a property whose value is fixed once you know the system's state — its temperature, pressure, amount, and so on — regardless of the path taken to reach that state. Energy, enthalpy, entropy, temperature, pressure, and volume are all state functions. Because of this, the change in a state function between two states is simply its final value minus its initial value.
This is enormously useful, because it lets you compute a change along any convenient imaginary route and trust the answer. It is also the deep reason Hess's law works. The honest caution is that not everything is a state function: heat and work are emphatically not — they depend on the path, like the distance you actually walked up the mountain.
Drive across town and your final location is fixed no matter which streets you took (a state function), but the petrol you burned depends entirely on the route (a path function).
Where you end up is a state function; how far you travelled is a path function.
A handy test: if a quantity's change is written as a clean final-minus-initial (like ΔT), it is a state function. Heat and work, written q and w with no Δ, are path functions instead.