Ok, this is it as clear as I can make it.
Maximum Authorised Mass (MAM) is the maximum a loaded vehicle or trailer can weigh including
Kerb weight is the weight of the vehicle ready to drive (ie has oil and coolant in) with a full tank of fuel, and not
loaded with either passengers or cargo.
So, if your car weighs 1000kg when empty (kerb weight) and has a MAM of 1500kg, you can carry 500kg in it including passengers.
What you can/can't tow without category B+E on your licence
The MAM of the trailer cannot exceed the kerb weight of the car.
The MAM of the car PLUS the MAM of the trailer cannot exceed 3500kg.
If the trailer is unbraked,the MAM of the trailer cannot be more than half the kerb weight of the car.
If a trailer has a MAM of over 750kg it HAS to have brakes.
Clear as mud yet?