IBM has a glossary that defines the word "state" in several different definitions that are very similar to one another. They don't specifically state that they are related to Object Oriented Programming but one can extrapolate and use them in that context.
Def 3: A stage in the lifecycle of an object that identifies the status of that object.
Def 5: A condition or situation during the life of an object during which it satisfies some condition, performs some activity, or waits for some event.
Def 8: An object's characteristic that is manifested in its public and private data members, and can be divided into two categories: essential state and non-essential state.
Def 9: In a business state machine, one of several discrete individual stages that are organized in sequence to compose a business transaction.
Def 10: A condition in which the circuit remains until application of a suitable pulse.
Webster's New World College Dictionary defines 'state' as:
A set of circumstances or attributes characterizing a person or thing at a given time; way or form of being: condition
The common denominator of all these is time. State changes as time progresses. That is the nature of variables. If someone were to ask, "What is your current state?" You could say today that you are married and tomorrow you could be single.
Considering all these definitions one can extrapolate that 'state' is the way that an object exists at a particular point in time determined by the values of its attributes, namely it's properties/variables.
I don't think it gets any simpler than that.