can any one tell me what this pump does and why it would keep running after i shut the boat motor off,or if it should keep running for a period of time

Looks like a bilge pump to me.  Pumps water out of the hull back into the lake.  Bilge runs off your battery.  I only turn mines on if I need to remove water out of the hull while I'm still fishing.  I'm still a boating greenhorn.  Other more exp'd guys will give you a better explanation. 

Yeah either a bilge or a livewell pump.

If it is a bilge it might have a float switch that turns it on automatically when ever enough water gathers in the bilge. If it is working right it when it comes on water should be shooting out of the outlet out the back of the boat some where.

it never was on before today wen i just went out and started it up but wen i flip the switches for the live well and bilge pump i can hear each motor turn on well that one is still running

Looks like a "Rule" brand live well pump to me.

http://www.rule-industries.com/products/pumps/livewell_pumps/index.htm

http://www.basspro.com/webapp/wcs/stores/servlet/Product_10151_-1_10001_89263_225003005_225000000_225003000?cm_ven=bazaarvoice&cm_cat=RLP&cm_pla=89263&cm_ite=description_link

it never was on before today wen i just went out and started it up but wen i flip the switches for the live well and bilge pump i can hear each motor turn on well that one is still running

:-?

Do you mean when you turn each motor off that one continues to run?

Could be a bad on/off switch not switching off. If that's a bilge pump it's possible it's hooked to a automatic pump switch and that's stuck in the on position. Kinda hard to figure out what you've got with such a small picture.

it never was on before today wen i just went out and started it up but wen i flip the switches for the live well and bilge pump i can hear each motor turn on well that one is still running

:-?

Do you mean when you turn each motor off that one continues to run?

Could be a bad on/off switch not switching off. If that's a bilge pump it's possible it's hooked to a automatic pump switch and that's stuck in the on position. Kinda hard to figure out what you've got with such a small picture.

X2

I'm really not clear at to what is happening.

Automatic bilge pumps generally have a switch with a "Manual" and "Auto" position.

In "Manual" position, the pump will run constantly of course (till the battery runs down).

In "Auto" position you might never hear the bilge pump run until there's a buildup

of rainwater or wave water that trips your float switch.

But a triggered float switch would be accompanied by a water stream at the discharge port.

If you hear the bilge pump running without any discharge stream,

it could be a stuck float arm (in high position) or a faulty panel switch (uncommon).

Roger

Just on the off chance that it's a three postion live well switch, off is probably in the middle.

Well if you can see where it is connected to you can solve the mystery. Stick your head down there and look. 

You might check the panel on front of boat where trolling motor plugs in (if it has one) mine has a switch up there to trim the motor and run the bilge pump.

You might have separate livewell pumps for fresh water or recirc. Or it might be for pump-out. As was stated before, follow the hoses and that would be your first clue.

Okay I have to correct myself...Front panel on my boat has switches to trim motor and live-well recirc. No switch for bilge pump. Sorry.

it does have a switch on the front panel fir trim and LW but the LW switch is not hooked up i have to put in a new toggle switch