Short answer, yes there is an open world map to explore.
Longer answer is there are 8 maps in total spread across the world, covering the regions of Grasslands, Junon, Corel, Gongaga, Cosmo Canyon, Nibel, Meridian Ocean and Northwood.
On top of that you have places which are independent to those regions, for example Golden Saucer. That's where I am at the moment, so anything after the Corel region I can't comment on, but they are big.
Doing everything in the Grasslands region for example, the first area you have access to, took me about 10 hours. In terms of the original game, that's the period of time from where you leave Midgar until you enter the Mythril Mines. Rebirth still follows that general route - Kalm, flashback, Chocobo Ranch, acquire a Chocobo, cross the marsh, enter the mine, but of course there are collectibles, optional mid boss encounters, side quests and so on. Saying much more than that would be venturing in to spoiler territory I feel, as there are umpteen little bits dotted around to find and be surprised by.
The game does feel massive, and really fleshed out, with things having meaning behind them rather than being a mere tick box exercise towards completing a region. Dared I say it feels too big, daunting almost, especially as a gamer whose gaming time is now limited. At the same time though, I'm loving it, and don't want it to end.
Considering the vertical slice of the game as a whole, there are few other games I've played which come close to troubling the content available, the amount of systems, side activities, mini games...it's almost unbelievable. The obvious comparison would the Yakuza/LaD, I guess.