What it Is
Essentia is the "liquid", or tangible, form of magical energy, or, more specifically, an aspect separated from the item it originally constituted. Essentia, being in a tangible form as opposed to a more mystical, intangible form, cannot be used to recharge Wands, Scepters or Staves.
Essentia can be stored in a variety of mediums, including the Warded Jar and its variant, the Void Jar, Glass Phials, Essentia Tubes and Arcane Alembics, although only in its production, as they cannot be "stored" in them for practical use other than when it is first produced, and a myriad of other ways.
Where to find It
Almost every block and item in the base game or added by Thaumcraft contains aspects, which are what constitute Essentia. As such, Essentia can be thought to be found almost everywhere. However, Essentia only applies to the liquid and tangible form of aspects, and as such it can only be created as opposed to found, to which the actual creation of which can be located in the section below this.
Essentia can only be obtained directly from items by breaking them down in an Essentia Smeltery or one of its variants. Other than this, different types of Essentia can be acquired by breaking down compound Essentia into its component Essentia types using an Alchemical Centrifuge. Currently, these are the only two ways of obtaining Essentia in its directly usable and liquid form, but Essentia can be crystallized into its respective form to be used in normal, as opposed to Automated, Alchemy.
Essentia can be used for 2 sole purposes, yet one of which can be considered one of the largest in the game, arguably. Essentia is necessary for Infusion, bestowing a central item with the properties of the Essentia and items used, allowing for the creation of very powerful and useful items. The other purpose of Essentia, however, as stated in the above section, is in Automated Alchemy, via the Thaumatorium. Unlike traditional Alchemy, Automated Alchemy takes Essentia directly from any sources it is allowed to or finds available and directly infuses the catalyst chosen with the proper aspects it needs, cutting the need to use normal items and create waste as is normally during the course of traditional Alchemy. However, early in a Thaumaturge's career, this option can be more polluting, as without augmentation or innovation, the Essentia Smeltery is quite inefficient, putting out relatively large amounts of Flux.