Varactors are voltage-variable capacitors. The word "varactor" is a form of portmanteau.
Think of the varactor as a diode where you can vary its reverse-biased junction capacitance. Typically you can achieve a range where the capacitance doubles from one voltage extreme to the other, e.g. a varactor could supply between 1 pF and 2 pF. Varactors can be discrete devices (ask your favorite diode supplier) or supplied monolithically as part of a MMIC design (SiGe technology usually offers varactors).
While we wait for content on how a varactor works, here's information on how to make a voltage-variable phase shifter using varactors.