Competing with VISA and the others is their goal here.
I would assume primarily domestic cards (platinum, quicksilver, savor) will start being issued on the discover network, while travel cards (venture series) will not (initially) because of the high domestic and low international acceptance rate of Discover cards.
They also have some mutual acceptance agreements with JCB and China UnionPay and others. Just because there's no explicit Discover logo on a terminal/restaurant window doesn't mean a Discover card will actually not work.
It's not quite the reach of Visa or Mastercard, but international acceptance seems to be trending up.
I'm riding high on Cap1, personally.