It was said by sailors when they were drinking together. A "hatch" is the opening that leads to the part below the deck: to go below the deck you would need to go "down the hatch." In the drinking idiom, the hatch is compared to the mouth, and so you would throw the drink "down the hatch" into your belly.

The hatch is a very wide pipe in the wall. You can put bags of dirty laundry in the hatch from upstairs, and it will fall into a basket downstairs. It is also used for rubbish in blocks of flats. You put your rubbish down the hatch and that is the end of it. Such is the meaning. Brad's below is a lot more common though.

down the hatch Meaning humorous exclamation or toast, an alternative to ‘Cheers!’ or ‘Bottoms up!’ and generally spoken with a glass raised (Note The ‘hatch’ is the mouth down which the libation is tipped.) http://www.idiomdictionary.com/definition/down-the-hatch.html