This answer assumes you're plugged into shore power or a built-in generator. If you're plugged into a portable generator, there's a very different answer.
The ground connection is also called the safety ground. If absolutely everything in the RV's wiring and electrical devices is working correctly you won't get a serious shock with an open ground. When something isn't working correctly in the electrical system and wants to make the chassis "hot", the ground connection carries the potentially hazardous electricity away instead of it possibly flowing through somebody's body. The bottom line is: If the RV isn't correctly grounded, unplug it immediately and leave it that way until it's fixed. The problem could be in the outlet the RV is plugged into, or in the RV itself. Testing directly at the outlet the RV is plugged into should isolate where the problem is.
The tester is not able to directly determine if the RV is actually grounded. It deduces this condition from the relative voltages on the hot, neutral, and ground wires. There are other conditions that can cause a tester to falsely declare an open ground, but when it indicates open ground, the highest probability is that's what it really is.