We have to distinguish between a clear intuitive concept of a limit versus the formal definition of a limit, which is perhaps what you encounter in your textbook. The formal definition is the only definition that is reliable for purpose of proving things about limits. The intuitive definition is what most students learn first.Summary:: I need a clear, basic definition of the concept of a limit. Textbook language is never easy to grasp unless the student is gifted.
Furthermore, the phrase "definition of limit" is ambiguous. There are different types of limits. The outstanding feature of the intutiive definitions of limits is the concept of a process taking place in time or in steps. In the formal definition of limit there is no mention or need of such a process. For example, the formal definition (or its notation) may contain language such as "as x approaches", however there is nothing in the formal definition that defines a process called "approaching". If you need to work problems in a text book that require you to understand the formal definition (the so-called "epsilon-delta definition") of a limit, then you have to progress beyond the intuitive definition, but the intuitive definition is where you should start.