In the microcanonical ensemble, you select all states with a given energy $E$. Assume you get $N$ states with that energy. Because you need to conserve energy, only the states with such an energy can be visited by the system.
To this, you add the "principle of indifference", saying that the system spends the same amount of time in each state, and you get a probability distribution $$\rho \sim 1/N$$
So far so good.
In a way, the universe is a microcanonical ensemble, although pretty big. The total energy is conserved.
However, what happens if take a big micro-canonical ensemble with energy $E_0$, we cut a small parte of the universe, we allow it to exchange heat (and only heat) at constant temperature with the universe and see what happens?
Imagine the system we have considering has energy $E_1$ inside it. The rest of the universe has energy $E_2$. The only thing we know for sure, is that $$E_1+E_2=E_0$$ at all times, but because the small system can exchange energy with the outside, it can "borrow" some of the energy or it can give some of its energy, so that $E_1$ and $E_2$ can both change (but only keeping $E_0$ constant!).
The constraint that the total energy is conserved now only holds for the universe, but the small space we are considering can change its energy by exchanges with the universe. So it can fluctuate.
It can, but does it? In principle it could be that the small system is sort of micro-microcanonical: it stays at constant energy $E_1$ so that principle of indifference holds. But in the event that the energy fluctuates, indifference can not hold anymore as low-energy states will have to be favored. Hence the form of the canonical probability distribution allowing for states with different energy.
So now you ask yourself, can I quantify this? You basically take the global probability distribution. You marginalise it taking into account only the small sub-system you considered. You do some math under the assumption $E_1\ll E_2$ and find the Boltzmann distribution allowing for fluctuations. You will probably do it in detail in your course.
Similar reasoning goes for the Grancanonical where you can exchange particles.
Summing up, what is special in the canonical ensemble is that as it can exchange energy with the outside, it can populate states of higher energy than expected by borrowing energy from the outside, so the states are not indifferent anymore. Temperature gives you a measure of how much you can fluctuate. Everytime you allow you system to vary something (with some constraints) you get a different system which (if allowed by the constraints) can fluctuate and violate "indifference" (or rather, you need to "weight" indifference with some extra variable)