Refer to figure.
A vertical speed indicator (VSI) is a pressure instrument that measures the rate of change of static pressure in order to indicate a rate of climb or descent. The diaphragm (or capsule) inside the instrument is connected directly to the static pressure source, while the instrument case is also connected to the static source but through a calibrated leak, which causes the case pressure to change more slowly than the pressure in the capsule.  The VSI indications work in the following way:

• In level flight - the pressure in the capsule and in the case are the same, so the VSI reads zero. 
• In a climb - static pressure decreases so the pressure in the capsule will decrease but, due to the calibrated leak, the pressure in the case reduces at a slower rate.  This difference in pressures causes the capsule to contract which will indicate a rate of climb.
• In a descent - static pressure increases so the pressure in the capsule will increase but, due to the calibrated leak, the pressure in the case increases at a slower rate. This difference in pressures causes the capsule to expand which will indicate a rate of descent.