State function is a property (thermodynamical) of a system, which is related to its current state. The property can be a physical quantity that can be measured.
A state function does not depend on the path or method that the system has taken to reach the current state. Examples of state functions are Pressure, gas, density, temperature, Entropy - Enthalpy, Altitude, mass etc.
Certain properties of systems depend on the path taken by the system or process or substance. They are called path functions. Work done probably depends on the path taken. But internal energy is a state function.
Standard state of a substance is the physical phase of the substance at room conditions. That is at 25 deg. C temperature and 1 atmospheric pressure. The physical phases are usually liquid, solid or gas. Water, Mercury have their standard state as liquid.