Anchor of a boat hope you can help
I've been teaching my kids about pirates and when we were talking about pirate ships this morning I confused myself greatly.
When carrying an anchor a pirate ship (or any vessel with an anchor) is free to float about where ever the crew pleases, however once the anchor is in the water the ship is held in place.
This seems unusual as (according to Archimedes principal) the weight of the anchor when it's in the water is less than when it's on the ship (immersed weight = weight - weight of displaced fluid) so how come the boat can carry the anchor but as soon as the anchor hits the water the boat cannot move?
As you can see below the ship on the left can move freely, the one in the right cannot.

I thought of a few possible solutions but maybe I'm shooting in the dark here.
Initially I thought maybe the part of the anchor that curls out at the bottom is holding a large volume of water (much more than that which the anchor displaced) and so holds the ship in place, like a scoop.
The other idea I had was that maybe the anchor is on the bottom of the ocean but this seems absurd, I've read that the average depth of the ocean is around 14,000ft (obviously parts are much deeper) and a 30mm chain of that depth would weight almost 100,000kg, which not only seems like a lot for the boat to carry but also essentially adds to the weight of the achor itself, perplexing the question further still
Thanks for your time
 A: Most anchors have to "hook" into the seabed, so you will need a long chain (rode). In some cases, the rode can have several thousand feet and weigh 100 tonnes. But in most cases, ships won't anchor in deep water.
Note that the anchor's rode must be several times longer than the sea depth:

To remove the anchor, you just have to shorten the chain until it's vertical. Then you pull "up".
In deep water, see the: sea anchor, which is a kind of sea "brake".

A: The anchor is on the bottom of the ocean. It attaches to the seabed, as jinawee pointed out. In parts where the seabed is too deep to reach, they use a drogue or sea-anchor. Buoyancy doesn't really play a role in how either work.
A: The ship drops the anchor which, in virtue of the stock (rebatable or collapsible arm near the top, perpendicular to the plane of the flukes)(flukes = triangular "nails" which should grab the bottom if sandy or muddy, or hook to stony bottoms)
will, with the subsequent pulling of the vessel, dig one (or both) of the flukes into sandy/muddy bottom.
But this is the initial process.  The ship is not held in place by the anchor, but by the weight of the chain joining the anchor to the vessel. 
The safe norm is to let go three times the depth of the water in chain. if the weather is good and the current weak. In adverse conditions the ratio should be higher.
Once the anchor is on the bottom, and enough chain has been payed out (in modern ships by going astern with the engine after letting go anchor, to help keep the chain extended on the bottom) it is immaterial whether the anchor dug in or not.
It is the weight of the anchor and the long curve (aptly called a catenary curve in math and geometrym from ancient greek Katinis, chain)it describes, that keep the vessel in place.  If properly anchored, the chain and the curve act as a sort of spring, never transmitting the tension to the anchor.  An old maritime adage states that, properly done, and having enough chain, it is possible to anchor with a pin, instead of an anchor.
Enough chain should be payed out from the beggining. If this is not done, then the anchor will drag and the vessel can easily be lost.
