The Tyranids are an extragalactic composite species of hideous, insectoid xenos. They actually comprise an entire space-faring ecosystem comprised of innumerable different bioforms which are all variations on the same genetic theme.
The Tyranids are unlike any other intelligent species encountered by Humanity. They are the ultimate predators; to them, all living things, from the lowliest insect to the most advanced starfaring civilisation, are mere prey. Only now are the inhabitants of the galaxy realising the scale of the threat; unless the Tyranids can be stopped, it will mean nothing less than the extinction of all life.
A Genestealer Cult is a xenos-worshipping secret society made up of and controlled by Tyranid Genestealers that thrives in the dark corners of the Imperial underworld across the galaxy. Secretive, stealthy, and utterly malignant, Genestealer Cults are the cancers growing unseen in the hidden spaces of Mankind's realm.
Their purpose is to rise up and take control of Imperial worlds in the name of a xenos god that is actually a Tyranid Hive Fleet. Once the world is under their control, the cultists' psychic emanations are picked up by the closest Hive Fleet's extension of the Hive Mind which is then drawn to consume the world, cultists and all.
A Hive Fleet is a large armada of living, biomechanical starships created by the Tyranids for the purpose of gathering the raw materials and biomass necessary for the reproduction, evolution and expansion of their species. A hive fleet is used to attack and strip star systems of their biomass using the full range of Tyranid bioforms.
A Genestealer Cult is a community of Genestealers, genestealer hybrids, as well as the completely human convert-hosts, infected victims and genetic relatives known as Brood Brothers, existing within another society.
Genestealer cults form if a Genestealer infects members of another species with its genetic code. The resultant changes in the genome of the host cause a fanatical loyalty to the genestealers, as well as a drastic change to their reproductive system; their firstborn children will be hybrids, a grotesque mixture of the host's race and genestealers.