The microbrain is the name given to an inorganic lifeform found during terraforming of Velara III.
When a small group of scientists began to terraform the planet Velara III, lead by Kurt Mandl, they noticed that areas of the sand looked like "the light shining off newly fallen snow." These shining patterns soon became less random, however, and formed geometric shapes and moved. It was later realised that this was a form of communication; however, as the Federation had declared the planet lifeless, the terraformists weren't looking for life, and dismissed it.
This changed in 2364, however, when Arther Malencon is killed in what appears to be sabotage in the laser drill's programming. Upons investigation by an away team from the Enterprise-D, Data discovers a single-celled compound, with glowing properties. Despite being inorganic, it is defined as alive when it reproduces on the Enterprise. Further, it appears intelligent when it connects to the Enterprise's computer and attempts to communicate via the universal translator.
The lifeform continues to reproduce and gain more control of the computer, securing environmental controls and deflector shield and transporter energy directed towards it. It is theorized by Data that the lifeform is akin to a computer, becoming more sophisticated as it reproduces further. It expends an enormous amount of energy during reproduction, with no little sign of energy loss from the ship's systems, leading to Data and Geordi La Forge realising the lifeform must use light energy to keep itself alive. This is corroborated further when it is discovered that the lifeforms on the planet live in an area it refers to as 'wet sand' - a soil layer near the water table, but where light still shines through. The water contains a saline solution, and each lifeform is connected to every other through this - forming a sophisticated collective conscienceness. This was threatened when the water table was being siphoned and clensed, leading to them declaring 'war' on the 'bags of mostly water' - humans.
This war ended shortly afterwards when Captain Picard darkened the lights in the medical lab where the sample of the lifeform was being studied and taken control of various systems. Picard convinced the microbrain that they were unaware of life on Velara III, and will leave the planet in peace if they call of the war. The microbrain agree, believing Picard's sincerity yet deciding not to trust humans for a period of three centuries, agreeing to see them again then. To that end, Picard orders a quarantine around the planet. (TNG: "Home Soil").