It pumps air into the exhaust, when the SAP is on the DME is adding extra fuel to create a very fuel rich mixture. This fuel rich mixture doesn't combust completely and in the exhaust it meets the fresh air from the SAP and burns again, causing the catalytic converters to get to operating temperature very quickly.

It can be deleted with no ill effects and still pass emissions in at least most states (CA and states following CA emissions I am unsure).