A state function is a property of a system that only depends on the (current or initial/final) states of a system, not its full history. Temperature would be a state function as it can be calculated by without determining how it reached the final temperature, i.e. the exact steps of cooling and heating are irrelevant, only the initial and final states. On the other hand, work cannot be a state function since the amount of work done depends on the path by which an object was displaced. Since internal energy is a state function but work isn’t one, by the first law of thermodynamics heat cannot be a state function either, since otherwise work could be calculated by two state functions, which would contradictorily render it a state function too.
By convention, thermodynamic properties of a system that are state functions are usually denoted by capital letters. Those that are not state functions are denoted by lowercase letters.