In a recirculating fluid system, contaminants will build up over time as the fluid is reused. Blow down is simply bleeding the system down to reduce the concentration of contaminants.
For example, if you kept adding oil to your car engine without ever changing the oil, the contaminants would concentrate until your engine oil was a sludge.
With a boiler, the boiler system is closed and salts will accumulate in the blower over time as water is heated and turns to steam (leaving the salts behind). If the concentration of contaminants is too high, then the contaminants will plate out inside the boiler on the heat transfer surfaces and destroy the boiler. That is why boiler blowdown is used to control the salt concentration within a set operating range. You can do the blowdown continuously or as a batch process.
In a cooling tower system, water is evaporated in the cooling tower which also leaves the salts behind. A blowdown process is also used to control the salt concentration in a cooling tower recirculation system.