When something proliferates, it's growing, spreading or multiplying really quickly. Bunny rabbits have a habit of proliferating, as do dandelions in untended gardens and funny YouTube videos on the internet.
Proliferate was originally a biological term used to describe the growth of cells and producing offspring. It wasn’t until 1961 that we started to use proliferate more generally to talk about everything from the spread of nuclear weapons to the wide growth of Walmart. Other similar words include expand, reproduce, snowball, and spawn.