Does this mean that up to 3 additional people can stay in the room (overnight) or does it mean that you can only have 3 guests additional to who has booked the room but they can't stay overnight?
It is hard to enforce but the idea is to not have too many people in a standard hotel room. For example, it would deter a group of 6 people trying to book a 2 queen standard room with four people sleeping on the beds and two people in sleeping bags on the floor. Not only would the room be pretty uncomfortable, it could be a hazard in the event of an emergency.
It is the number of people allowed to stay in the room. You can have people over, but in terms of actually staying there with their stuff and sleeping there, they only allow so many per room regardless of beds.
I have seen 10+ people in one room before. They have a hard time enforcing it, especially when people get drunk. I think some hotels are more strict about it than others. It is more or less a safety and health hazard issue but you know it has to do with money as well!
To my knowledge, it's the amount you can have in your room, but they are not allowed to stay. I remember one of the first times in Vegas, I stated with my brother and sister-in-law, and their two kids, so I probably made it too many people in the room. They didn't know, but it was scary sneaking in.
So yeah, I think it implies that you can have up to 3 guests for a while, but they can't stay the night like others in this topic stated.
"Max Guest 3" would imply that you can have in addition to, an extra 3 guests max. Say you and your spouse, and maybe your kids are staying. If you paid for them, that means they can be there, and an additional 3 guests max can also come by. I don't think it means they can stay though.