Conceptual modeling, is a way to describe applications and to structure information databases, this definition is from the article [1] by Alex Borgidia and Ronald J. Brachman.
In the book about Generative Programming: [2] a concept is described as something that is recognized by having certain properties. An object can for example be recognized as being an instance of a concept by having certain features that the concept is known for. Conforming to [2] concepts can be classified as either mathematical concepts or natural concepts. Mathematical concepts are numbers, geometric figures, matrices etc. All mathematical concepts have a precise definition, while natural concepts are less precise. Natural concepts are used in our everyday communication and can be described in our natural language. Concepts can be described by their properties, there are two mayor types of properties when describing concepts: features and dimensions. Where features represent the qualitative properties of the concept, and the dimension represents the quantitative properties.
In the article [3], a conceptual model is described as: A conceptual model is a formal model in which every entity being modeled in the real world has a transparent and one-to-one correspondence to an object in the model. Conceptual models map directly between real world entities and programming objects, describing real world entities as objects with attributes, where the attributes are modeling the entity's features. Because of the models near resemblance with the real world and our perceived understanding of the elements in it, the model is easy to understand for humans and a good base for implementing applications as they are semantically transparent to users who are familiar to the problem domains.