When you’re driving around every day on paved roads, it helps to have your tires pumped up to the recommended PSI. It saves you gas, and it’s easier on your car. Once you decide to go offroad and start dealing with uneven surfaces, deflating your tires gives them a bit more slack to sink into something.
For an example, let’s imagine you’re trying to drive over a large branch. Your tires are pumped up though, and when you can’t make it – they start to spin. As your tires rub against the branch there is no give, and they do not conform to the shape of the object they’re trying to move past.
In the same example, let’s imagine you have properly deflated tires. You approach the branch and instead of your tires spinning against the object – the slack provided by less air allows your tire to “grip” the form it needs to overcome.
As you can see this is a huge advantage when it comes to offroading.