Lua is a scripting (programming) language developed in Brazil in the 90's that is used in developing embedded systems. The TI-Nspire supports and uses Lua in it's operating system. A Lua Script Editor is included in the computer software. In addition there are two utilities (documents) that allow you to write and test Lua programs right on the handleld TI-Nspire.
Writing a Lua program amounts to creating a custom app (application) that can be used in addition to the built-in apps of the TI-Nspire. The custom app can communicate with the other apps in your problem through variables so that content in one app will affect the others.
This page contains a collection of resources that I find useful as I learn to tap the power of creating my own apps for the TI-NSpire.
See my TI-Nspire page for some samples of Lua scripting.
Here's a small collection of Lua resources...