A state element is a logical unit that stores a value and contains at least two input values and one output. The inputs are data inputs that can be written to the state element, which itself has the capacity to store data.
The state element will have data written when signaled by one of the inputs, such as a clock signal, and can be read at any time.
CPU registers are excellent examples of state elements—they are small units of memory that, depending on input signals, may contain different data at any state in time. The output, able to be read at any time, will reflect the current state of that memory element.