An answer has already been accepted, but I'd like to share what I believe is a more intuitive explanation.
There are many risk neutral probabilities ... probability of a stock going up over period $T-t$, probability of default over $T-t$ etc.
The intuition is the same behind all of them.
In reality, you want to be compensated for taking on risk. This is why corporate bonds are cheaper than government bonds. In risk neutral valuation we pretend that investors are stupid and are willing to take on extra risk for no added compensation. The reason is it make the math easier. The intuition is to follow.
Let's consider the probability of a bond defaulting:
Imagine a corporate bond with a real world probability of default of 1%. This 1% is based on the historical probabilities of default for similar grade bonds and obtained form a rating agency. If the bond defaults we get 40% of the par value.
If we try to price the bond using only the real world probability of default given above to calculate the expected value of this bond and then present value it, we will come up with the wrong price. In fact, the price will bee too high.
Why? Because the bond's price takes into consideration the risk the investor faces and various other factors such as liquidity. We've ignored these and only have part of the picture.
Enter risk-neutral pricing. Instead of trying to figure out these pieces we've ignored, we are simply going to solve for a probability of default that sets PV(expected value) to the current market price. This is called a risk neutral probability. Well, the real world probability of default was 1% and just using that to value the bond overshot the actual price, so clearly our risk-neutral probability needs to be higher than the real world one.
I've borrowed my example from this book. I think the author gives the best explanation I've seen https://books.google.ca/books?id=6ITOBQAAQBAJ&pg=PA229&lpg=PA229&dq=risk+neutral+credit+spread+vs+actuarial&source=bl&ots=j9o76dQD5e&sig=oN7uV33AsQ3Nf3JahmsFoj6kSe0&hl=en&sa=X&ved=0CCMQ6AEwAWoVChMIqKb7zpqEyAIVxHA-Ch2Geg-B#v=onepage&q=risk%20neutral%20credit%20spread%20vs%20actuarial&f=true.