Intentionality was first developed by Franz von Brentano. His student, Edmund Husserl, make it part of his doctrinal base of phenomenology. I want a clear and modern definition of intentionality.
Dagfinn Føllesdal, "Husserl's Notion of Intentionality." In John Macnamara & Gonzalo E. Reyes (eds.), The Logical Foundations of Cognition. Oxford University Press USA. pp. 296-308 (1994)
That article might provide what you're looking for vis-à-vis Husserl. As for a "clear and modern definition", well, things have gone way beyond Husserl, with too many twists and turns and lots of failed attempts at providing necessary and sufficient conditions. I'd suggest starting with John Searle's book, Intentionality.
For some of the failed attempts see
Article Intentionality and the Non-Psychological
Article Chisholm on expressions for intentional relations
I think- Intentionality is a prediction of the state of mind, affected by occurrence or non-occurrence of incidents depending on the age, place, and intelligence of a person. It deals with attempts and practices prevailing in the surrounding, regardless of success or failure. It is a life-long automatic process.
Intentionality, as used by the philosopher Edmund Husserl, refers to the directedness of mental acts or states towards objects or states of affairs. In other words, it refers to the fact that our thoughts, perceptions, and experiences are always about something or directed towards something.
Husserl believed that intentionality is the fundamental feature of consciousness, and that all conscious acts, such as perception, thinking, and willing, are intentional acts. He also believed that intentionality is an irreducible feature of consciousness that cannot be reduced to anything else. Husserl argued that this directedness of consciousness towards objects is a fundamental feature of our experience and that it is what makes it possible for us to know the world.
In Husserl's phenomenology, Intentionality is the foundation of all meaning and understanding, it is the act of consciousness that posits or directs itself towards an object, giving it meaning and sense. He also claimed that the intentional act should be distinguished from its object, as the act of consciousness is separate from the object of consciousness.