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Mental processes can not be observed directly, because all psychological concepts and labels, like learning, memory, motivation, personality, etc, are inside your mind/brain. Therefore, to study and measure them you need to measure something that reflects these processes. These "stand-ins" for mental processes are called operational definitions.
Operational definitions define concepts and labels by the way they are measured. For example, an operational definition of weight could be: how much a spring stretches when you hang something from it, or how many pennies it takes to balance the weight of something. All psychological concepts and labels, like learning, memory, motivation, personality, etc, are theoretical concepts, which cannot be measured directly.
For example, the operational definition of temperate is how much a column or mercury or red colored alcohol expands in a thin tube put in the thing whose temperature you want to measure. In 1714 Gabriel Fahrenheit defined 0 as the temperature at which a concentrated mixture of salt and water freezes and +96 as the temperature of the human body. In 1741 Anders Celsius defined 0 degrees as the freezing point of pure water and +100 degrees as the boiling point of of pure water at standard ("sea level") pressure, the scale that most of the world outside the US uses.
In contrast, a theoretical definition is based on a theory. When the theory of heat as atomic motion was developed, a theoretically based scale, called the Kelvin scale, was created. The Kelvin scale's 0 degrees is the temperature at which all atomic motion (theoretically) stops. Keeping the step size created by the Celsius scale, the freezing point of water is 273 degrees Kelvin and the boiling point of water is 373 degrees Kelvin. Physics and chemistry have powerful, well-developed theories, so (most) measurement is done using theoretically based scales. Psychology is much less fortunate, and has only a few theoretically based scales.
Link to a chatty, practically oriented explanation of operational definitions and to a detailed, formal explanation of operational definitions.