I bought a house built in 1891, which has much of the original detail.
The hardwood floors are unique because you can see the nails. They are
not parquet, but rather arranged like contemporary floors all in the
same direction and using long pieces of wood. But you can see the nail
prints in each piece of wood, and they also have a wooden border all
around the room.  What is the name for this technique?

I believe it is called ship's plank flooring:
http://www.plankfloors.com/ships_plank_formal.html
http://www.parkettborse.com/products.htm
"scroll down to the bottom of the second site)

Having visible nailheads is unusual and not part of the definition. 
As you have probably discovered, after a century the heads and
surrounding wood may stand above the rest of the flooring.

Thank you for this.  with this lead, i searched some more and found
that some definitions of ship's plank DO include the nails.  see
http://cherokeewholesalers.com/boen-hardwood.php?item=140&x=2&type=1&s=AnlBh1UGWzOp
that talks about treenails.  and the picture at
http://www.skagerak-denmark.com/gb/floorings/cat506_239.asp is pretty
much exactly what i'm referring to.  thanks much.

You did not state where you live, but from my experience your type of
floor is not unique in the latter 19th Century.  If you are going to
sand these floors, make sure you drive the nails in further and then
sand the wood down to the nails.  Otherwise, you will sand the heads
off the nails.

Yeah, or more likely, the nails will eat up your sander.
Treenails:
"A cylindrical pin of oak, or other hardwood, used to secure the
planks of a wooden ship to the ribs. They were used instead of metal
nails or bolts because they did not rust or loosen or because metal
was not available yet. Was pronounced as trennel. ***"
www.ageofsail.net/aostermi.asp