If a definition is supposed to help us better understand a concept, theoretical definitions are those which do the most heavy work in that regard. Lexical definitions try to help us understand how a concept is used, but theoretical definitions try to help us understand how a concept is and should be used in all cases. Theoretical definitions occur whenever we try to characterize all entities or examples of a particular type thing or concept; they are usually seen in philosophy or science, and they can be among the most difficult to fully comprehend.
An example from philosophy would be a discussion about the nature of love any attempt to define love in a way that includes all actual instances of love while excluding all instances that arent really love would be a theoretical definition. An example from science would be an attempt to define cancer in a way that eliminated any vagueness and any borderline cases, thus making clear exactly what is and is not truly cancerous.
The reason such definitions are called theoretical is because the definitions themselves attempt to construct a theory about the nature of the thing in question. Thus, a theoretical definition of justice is not simply an attempt to point out what justice is or report on how people happen to use the word, but instead an attempt to create a theory which argues for a particular conception of justice.
Theoretical definitions are, for this reason, closely related to persuasive definition. They differ from each other because the theoretical definition does make use of regular lexical definitions, but at the same time it also tries to persuade people to adopt some particular position on the nature of the thing in question. Theoretical definitions may be presented in a neutral manner, but they are created with a specific agenda and purpose in mind.
Theoretical definitions are also similar to stipulative definitions because they propose a new understanding of the concept involved a new theory which adequately explains the concept in all of its senses. Thus, like stipulative definitions, a theoretical definition cannot be judged true or false, accurate or inaccurate. As proposals to understand an idea in a new way, theoretical definitions may be useful or not, fair or not, even fruitful or not but accuracy is not a relevant attribute.
More: What are Definitions?