A capacitor consists of two parallel conducting plates separated by an insutaing material called dielectric.
Its stores charge in the form of electric field.
It has many uses like filtering, time base generatin, DC-isolation etc.
Capacitor alone does not make any changes to waveform if it is passed through it but when used with inductor or resistor, it forms lead or lag network introdcing phase shift in the waveform or even change in its characteristics. Differentiator/ Intergrator are such circuits which results in differentiated/integrated waveform at the output.
For more details, read this tutorials: **broken link removed**