Some areas will be closed off at release in order to make room for expansion, and initially you will be restricted to your faction territories, so a Khajiit cannot go to Skyrim and a Nord cannot go to Orsinium. But after you reach level 50 you will be able to go to a phased version of those enemy territories but no enemy players will be present.
To my understanding you will be able to "Explore" all of Tamriel. Now some of it will have to be after you hit 50. But I'm sure they've said that we'll have access to all of it, regardless of Alliance.
The gray area on the map is for future expansions. That includes most of Elswyer, Morrowind Island, Skyrim area, the south east part of Cyrodil in Oblivion and some other.
You can enter other factions areas at level 50 to do their quests and explore