Having seen this question often on this platform, but never read a statisfying answer.
First of all, you should write your questions in a clear manner. It isn't clear what voltage difference you are talking about, whether there is an emf source or not etc.
But in general note that the term "parallel" in the context of electric circuits implies that the elements that are parallel have the same potential difference between their terminals. To elaborate:
Kirchoff's 2nd Law states that the voltage differences through a loop should add up to 0 meaning a charge should have the same potential energy that it started with when it comes back to its initial position. Note that this takes both energy loses through circuit elements and gains through emf sources into acount.
This means when you connect another capacitor it doesn't increase the voltage but you provide "extra space" for the charges to go. Since they are less dense, the same amount of charge will create a smaller voltage across the capacitors.
Or if you connect a battery, since there is more "space", you can store more charge using an identical battery.
This "space" is the capacitance of the capacitor and it determines how much charge it will hold for a certain voltage. And when you add another capacitor, you increase this space. To be precise, the equivalent capacitance value is the sum of the capacitances of our original capacitors.