When you are new at sap developments, a brief overall description of the Transport system can be useful. The Transport system is there to move your developments (or whatever other damage you or anyone else can do in SAP) to other systems. Roughly outlining this, it can be regarded as a huge interface system, but not only for data, also for objects like programs, menu's, screens, transaction codes, authorization objects, anything you like. There's hundreds of types of objects available for transportation. Like in any interface process: a file is created, which will (eventually) be picked up by the importing system.
When addressing Transport & Correction, consider the following: changes that are done or corrections that are made need to become available in other systems. These changes can be (customizing) settings or actual objects that have been modified. Since a functional change can result in a range of technical object changes, the whole package of corrections need to be "moved" as a whole.
A serious task with serious impact and a serious suite of tools to help you get the job done...