What I know (which may not be right but...) about the secondary air pump is that it only has something to do with emissions coming from your tailpipe. Without the pump, your car may not pass emissions in certain states. If sometime you start up your car, and all of a sudden hear a rumbling sound coming from your pump, it'll get louder and louder until you get it fixed... I'm not sure what 'fixing' it means, if it means to get another entire pump or to just get all the water out. I actually sold my car without having to fix it as it wasn't acting up... but the owner who has it now will have to replace it in the near future probably... heh.
If anyone else knows about secondary air pumps I'd like to know.