Final answer:
The element that helps in the insertion of new data and the deletion of existing data in a database application is Data Manipulation Language (DML).
Step-by-step explanation:
The element from the given options that helps in the insertion of new data and the deletion of existing data in a database application is Data Manipulation Language (DML). DML is a language that allows users to perform operations such as insert, update, and delete on the database. It provides commands like INSERT, DELETE, and UPDATE to manipulate the data.
DBMS (Database Management System) is the software that manages the database. Although it provides a platform for data manipulation, it does not directly handle the insertion or deletion of data. Operational databases are databases that are used for day-to-day operations of an organization.