Essence is the genetic information carried by all life and is key to zerg evolution.  The zerg take the essence of their prey, either through consumption or assimilation, and in doing so, incorporate their prey's desired strengths into themselves. This unique ability to steal essence motivated the fallen xel'naga Amon to enslave the zerg during their uplifting on Zerus. The zerg are said to possess "purity of essence," along with other species over time. On Zerus itself, essence can be found in some bodies of water.
The amount of essence required for a successful evolution varies. For example, in order to evolve the creeper strain of the swarm host, only a single ash worm needed to be killed. However, in order to evolve the impaler strain of the hydralisk, multiple impaler colonies had to be destroyed before enough essence was collected. In other cases, essence from specific individuals of a chosen species - (e.g. an ursadon matriarch) must be collected to augment the Swarm appropriately.
The essence of each zerg type is stored in specific hive structures (such as the lurker den) and allows hives to spawn their various minions from larva. In the aftermath of Sarah Kerrigan's de-infestation and the subsequent fragmenting of the Swarm during the Second Great War, the zerg lost the essences of many of their strains. They were subsequently forced to seek out the lost strains amongst feral zerg, and re-assimilate their essences through capture or consumption. The corruptor's essence was completely lost and unrecoverable.
Some essences cannot be assimilated by the zerg— the protoss cannot be assimilated into the Swarm due to the protection the Khala and energies of the Void provide for Khalai and Nerazim respectively. Protoss genetic material itself cannot be used by the zerg. Hybrid essence, while strong, can also not be consumed. Terran essence is considered unimpressive by Abathur. While some terran individuals can retain their psionic potential and intelligence post-infestation, they are the exception rather than the rule.
The essences of the primal pack leaders on Zerus is visually akin to purple-white energy. After being reborn as the primal Queen of Blades on Zerus, Kerrigan slew the pack leaders and absorbed their essences.
Xel'naga essence is visually akin to golden energy. In accordance to the Infinite Cycle, the elder xel'naga would sacrifice themselves to transfer their essence to their chosen offspring, transforming them into xel'naga themselves. During the final stages of the End War, Ouros imparted the last of his essence to Kerrigan, transforming her into a xel'naga.