Here’s how this theory goes. If a society gets advanced enough they would eventually be able to create a simulation of their universe that would be extensive enough to cover everything down to subatomic particles.
Once a society gets this advanced, eventually they are going to run such a simulation, to test theories on universal evolution, or even societal evolution. Maybe even theories on sentience itself.
Now, if you happen to be a sentient within such a perfect simulation, how would you know? What test could you do that would prove that you are in a simulation? In the same breath, how could you prove that you are not? Simply put you could not.
Additionally we are seeing that with new exotic computing materials and techniques that it appears as though there is no real limitation on how much computational power you can get in one place, then it is inevitable that someone will eventually run this simulation.
Now that we know it is possible to simulate a universe such as our own we can logically agree that this means it is only a matter of time before someone does so and that it would be impossible to know if you were in a simulation or not.
This leads to the final question; is there a possibility that a species other than ours has reached this level of computational power ahead of us? If so, then is it possible that they have created such a simulation? If the answers are both yes, then we must logically conclude that we are in such a simulation.
Think of the Sims game. We were able to create that, and we could create something 50 times more realistic, and with better AI if we wanted, so basically people who believe that are saying “if we can create something like this’s who’s to say that we aren’t in a simulation like the one we created?”
Another argument is that our universe follows mathematical laws, and seems to show signs of optimisation to speed up computing (for example we have maximum speeds and minimum temperatures and a number of seemingly arbitrary constants defining relationships)
There is this explanation in comic form: