What elements of a capacitor make it higher voltage and higher capacitance
\$ C = \epsilon_0 \epsilon_r \dfrac{A}{d}\$

Where:


\$C\$ is the capacity in Farad [F];
\$\epsilon_0=8.854×10^{−12} \text{F/m}\$;
\$\epsilon_r\$ is 'relative permittivity', its value is specific for the material used as insulator. See also @rawbrawb's comment;
\$A\$ is the area of the plates that overlaps in square meters;
\$d\$ is the distance between the plates in meters.


So:


if the plate overlapping area increases, the capacity increases and 
if the distance between the plates increases, the capacity decreases.


The insulator that fills the space between both plates (A×d) has a limited strength when it comes to voltage between the plates. The insulator will breakdown at a certain maximum voltage, at that point it is no longer a capacitor, but probably a short.