Why is it harder to turn a motor/generator with shorted terminals?
I have to start with some terminology -- sorry if it's esoteric, but this will bring things into line with how folks talk about this subject.
When you turn a permanent-magnet DC machine*, the armature generates a voltage internally. This is called the "EMF"** of the armature, or the "back EMF" if the machine is running as a motor. This EMF is always generated when the machine turns.
When you run current through a DC machine, it generates a torque. This torque is always generated when the machine turns, regardless of whether it's a motor or a generator.
When you put a resistance on the terminals of a machine and turn its shaft, it generates that EMF. With the resistance connected, this EMF causes a current to flow that's proportional to the EMF divided by the external resistance plus the machine's armature resistance. This current, in turn, generates a torque that resists motion (due to conservation of energy, it must be in a direction to resist motion).
Shorting the machine puts the smallest possible resistance on it -- you can't get lower than 0 without resorting to active circuitry. The back torque in this case is purely a product of the EMF and the armature resistance. Increasing the resistance by putting a resistor on there means less current for the same machine speed, which means less back torque. In the extreme, you have no resistor at all, which means infinite electrical resistance -- this means that the back torque will be from mechanical effects such as friction (and windage, if you're turning it that fast), and possibly mechanical and electromechanical effects as the field magnets work against the iron in the armature.
* I'm calling it a "machine" instead of a "motor" because it can be a motor or a generator, depending on how you use it. But you don't have to change anything internally to change how it's used -- hence, "machine".
** EMF stands for "electromotive force", which is just and older term for "voltage". It seems silly to have two terms, but sometimes it's useful.
"applying a resistive load" to a running motor is essentially how an electric brake works. As a first approximation, the torque produced by the motor is proportional to the current, that's turning the motor is harder as the load resistance gets smaller. When you short the terminals, there's only the internal resistance of the motor which limits the current.
As I read the accepted answer my brain came up with the following simplification, which I think is loosely accurate (?):
Motors are both dynamos and electromagnets.
Turning a motor invokes its properties as a dynamo.
Because the motor's terminals are shorted together, the generated voltage is applied to the motor coil windings, invoking the motor's properties as an electromagnet on its own axle.