Secondary air injection systems are used for emissions purposes, where extra air is injected into the exhaust stream of an engine to burn the leftover fuel in the exhaust stream. This is because there's always some fuel that isn't burnt during the combustion stroke. So, to meet emissions regulations, the smog pump injects air into the exhaust, where the heat and pressure burns the fuel.
Even though it's technically not necessary to have a secondary injection system for a car to run, improperly removing it can do more harm than good. The air introduced to the exhaust through the smog pump allows for the exhaust to maintain constant pressure, which is necessary for smooth engine performance. In addition to this, when the engine is cold, the extra air introduced to the exhaust and the subsequent burning of the extra fuel helps the catalytic converter reach operating temperature quicker, which improves its emissions reducing performance and extends its life. However, there are ways to properly remove the secondary air injection system for performance reasons. By purchasing a kit online, the smog pump can be removed, while still retaining proper exhaust pressure; although, the benefit to the catalytic converter that a secondary air injection system provides is lost.