Simple definition of Agile is given below along with the key terms highlighted. Take a look-
Time-boxed means all the activities/iterations/ceremonies are time bound. There is no endless, limitless time approach. At the end of the defined time limit, desired output should come which is crucial.
Iterative model is a successive upgrade for a project. For example if we have to make a greeting card, we should first create the frame, draw the figures, colour it and then decorate to complete it. It has to step by step in a proper flow.
Incremental is piece wise delivery. With the same example, if we are making a card incrementally, we shall create one part of card completely and then increment it with next small part and it will go on till the completion stage. This simply implies making the card for eg, in stages but the point worth noting here is that each stage is complete in itself and proceeds to the next addition thereon.
This is defined by the relevance and need of the feature for the customer and the business. As the need increases so does the business value as they complement each other.
Agile is a combination of all these. Where by following time-boxing, we incrementally iterate and release potentially shippable product after every iteration; this potentially shippable product is the one driven by business value as the features in it are prioritized by Customer as per their requirement and business needs.
Focus on Business Value is a core aspect of Agile. At the end of iteration, the amount of work is achieved with a quantum of value delivered. Potentially Shippable Product with a business value delivered with it in each increment is of foremost importance in an Agile based environment.