Conspiracism is a philosophy of the modern age, a way of thinking that explains the frustratingly random world around us with the idea that it's all happening for a reason.
Unlike with religion, in conspiracism intelligence behind all this isn't divine or supernatural, but very human: extremely powerful, secretive people with immense resources, selfish motives and the willingness to manipulate everyone's lives towards an ill-defined goal of world supremacy.
All arguments against the conspiracy theory are used as evidence of the cover-up essential to the conspiracy's existence. The government has photographic proof of the moon landing? It must be planted. The President actually produces the certificate proving his place of birth? It must be a fake. Someone who knows exactly what happened explains it all in detail? They must be lying.
Conspiracy theories are seductive and infectious. They allow the believers to explain all the things wrong with their lives in a way that doesn't put them at fault. It makes them part of a special club of people who know The Truth.
And perhaps above all it gives them a way to make sense of an unfeeling and directionless world, even if it does so in a way that is profoundly terrifying.