thermodynamics - Entropy is...disorder?

As I read somewhere, it said that the universe is heading toward disorder a.k.a entropy increasing.

Now as far as I know from the second law of thermodynamics it states that entropy is indeed increasing and in the end, the entropy of the universe will be maximum, so everything will evolve toward thermodynamic equilibrium (e.g same temperature everywhere in the universe).

So my question is: isn't equilibrium order? Why is entropy called a measure of disorder if more entropy means more order?

Answer

What you are missing is the microscopic definition of entropy, once you know that, you will understand why people say that entropy is disorder.

Equilibrium as order

First, let's address your valid intuition that equilibrium as a form of order. Indeed, if everything is in thermal equilibrium, you just need to measure the temperature somewhere, and then you will know the temperature of everything. In our out of equilibrium, my body, my laptop, the room, outer space, all have different temperatures, and I need more information to know the state of everything, and I feel this is less "ordered" than the thermal equilibrium case.

What transpires is that less information needed corresponds to a higher degree of order. Well, let's keep that in mind for the next bit.

Entropy is microscopic disorder

In Physics, we know that the properties of macroscopic objects are determined by the motions of the particles that compose them. In particular, temperature of a gas is the disorganised jiggling of the atoms making it up.

As you increase the temperature, the atoms will move more and more erratically, and will have diverse speeds at any given time.
As you cool it, the particles will move slower and slower, until perhaps they freeze in place, forming a solid.

Which of the two - the still, regular lattice of the solid or the whizzing commotion of the particles that forms a gas - seems to you more disordered? Definitely the second. You know from thermodynamics that the gas has higher entropy than the solid. Indeed, there is a precise formula linking the macroscopic state variable $S$, entropy, and the microscopic conception of disorder I described.

Conclusion: the two ideas are reconcilable

In the projected "heat death" of the universe, everywhere there is constant temperature and density. In that sense, the universe is homogeneous and thus ordered. But microscopically - in the movements of the particles - that is the state in which there is the least order: no structure whatsoever, just a big soup of whizzing particles.