Does it make a noise at all when you run water?

Why not open the cover and have a look?

Yeh it makes noise when running the water.
I was thinking its a water pump?

Yeah looks like a potable water pump to me 

If it makes noise when you use water, then it most likely contains a pump, small pressure tank and a pressure switch. They're usually used for tank water, but there's no reason you can't use one to boost water pressure within the house.

I'd definitely open it up to have a look. There may be parts that need maintenance. If one of those pipes is an inlet, it may be a little on the small side for the pump. Generally, pipes going in should be as large as the diameter of the pump inlet.

Is it to help the stormwater/sewage discharge out to the street? 

i.e. mains water is fine, but the discharge needs a hand due to "go".

ice2004:

Does anyone know what is this? and what is the purpose?

It seems to be water pump, I have water tank in West Auckland.

Was doing some tests running the laundry water or the tap outside which has sign that says recycled water but the water meter still runs, so does the water from the tank gets pumped and also the water from main also gets pumps to keep the water pressure consistent? still saving water?

I know you shouldn't just assume its a pump, but it does say "Wallace Pumps" on the top of the cover! https://www.wallacepumps.co.nz/household-water-supply.html 

You'll have to take the cover off to see exactly what pump setup you have.

Do you know if there are any other tanks under the house? Can you trace where the pipes come/go to?

Yes there is a water tank, I think it is water pump because whenever I open the water it starts like making noise and once I close water it stop, doesnt make any noise.

Is that power plug rated for outdoor use ?