Thaumcraft is a mod created by Azanor. The version included in the FTB mod pack is Thaumcraft 3, which is a completely different mod than Thaumcraft 2. Thaumcraft focuses on the unseen magical auras that exist in the Minecraft world. From the Thaumcraft 3 site: "This is what this mod is all about - drawing magic from physical objects in the form of Essentia and reshaping it to perform miracles."
Thaumcraft 3 has now been updated to Thaumcraft 4, which is entirely different.
Aura vs Flux
Aura is the natural ambient magical energy of the Minecraft world. It is held within Aura Nodes placed throughout the world, as well as within Infused Ore. Each Aura Node has a base amount of energy it can contain. The Aura can be tapped into by a Thaumaturge and harvested for its energy, known as Vis. If an Aura Node is not at its base value, it will attempt to balance itself, drawing energy from other nearby Aura Nodes or Infused Ore. During this process of re-balancing, the node will randomly generate Flux, a form of magical disturbance. As the auras attempt to return to order and balance, Flux will be purged, which can have various impacts to the land and inhabitants surrounding the node, including bad weather and inducing Nausea on the player. The most common form of Flux relief is the creation of magical creatures known as Wisps.
Most items in Thaumcraft are not craftable in a standard crafting table to start with. Instead, Thaumcraft makes use of a research mechanism that unlocks items by discovery.
The mod intends the player to learn the recipes by intuition, research, and sometimes just plain trial & error. It is advisable to attempt to figure out how the research system works, as that is a major aspect of the mod, rather than spoil it by referring to the FTB wiki. If you would like a non-spoiler introduction into research in Thaumcraft, use the Getting Started (Thaumcraft) guide. For a full list of discoveries and the Essentia required for each, use the Thaumcraft Research and Discovery guide.