state function - it doesn't matter the path you take to get there, you will always arrive at the same spot.
Example: If I want to have $1000 in my bank account, I can add 200/week until I have $1000 or I can add $750 one week, $500 the next week, and then take out $250 and I'll still have $1000. No matter which way I did it, I still have the same ending amount.
Non-state function - the path you take makes a difference in where you want to end up or what the values will be.
Example: The distance between two cities depends on the path you take. You can take a direct route and be there in 20 miles or you could take a bunch of side roads and be there in 50 miles. Your distance traveled will be different in each case.
In terms of chemistry, pressure, volume, temperature are all state functions. Heat and work are not considered state functions individually, but their sum, delta E, is.