What does a capacitor do?
I would love a clear explanation (not just mathematical formulas)

Well, it starts with the basic capacitance formula so, if I add enough extra words, it should hopefully comply with your request. Here's the basic formula: -
$$Q = C\cdot V$$
As an analogy, consider a glass of fluid: -

Picture from here. So, charge is how full the glass is. And there's an old saying when making a toast to someone: -
Ladies and gentlemen, please charge your glasses 

Source
Then, did you know that the rate at which Q changes (how quickly or slowly you pour fluid into the glass or empty fluid from the glass), is related to how quickly the top level of the fluid rises or falls (again based on the previous equation Q = C.V): -
$$\dfrac{dQ}{dt} = C\cdot \dfrac{dV}{dt}$$
And, for EE, the rate of change of charge is current or, in the glass/water example, it is how much fluid per second you are filling the glass, hence: -
$$I = C\cdot \dfrac{dV}{dt}$$
So, think about the glass and the rate of change of fluid and the cross sectional area of the glass (capacitance). If the cross sectional area is large it takes a lot of fluid to fill the glass to a certain level. It's the same with a capacitor; to raise the voltage on a bigger capacitor you need the same current for a longer period of time. Or, to fill it in a shorter time, you need more current.
So, a big capacitor will take a lot of current to raise the voltage in such and such a time. This means it acts like a low impedance if you are wanting to raise the fluid level quickly and, it acts like a higher impedance if you want to raise the fluid level more slowly. If you don't need to change the fluid level you don't need to add or remove fluid and this is why a capacitor is good at holding a DC voltage constant because it takes no current to do so.
Regards your op-amp circuit, it's probably a step too far because you need to demonstrate that you understand virtual grounds and negative feedback: -

@Andyaka I don't really understand the negative feedback – Ralph Aouad

Then begin at a simpler level and work out why an op-amp MUST produce a virtual ground at the inverting input of a simple unity gain inverting amplifier that uses two equal value resistors. These Q/A might help: -

The op-amp as an error amplifier
Operational Amplifier Voltage Stabilization
What is the purpose of an opamp in an integrator circuit?