This pass comes in four different forms: you choose either small area or wide area, and whether you want the airport limousine route (and an extra two days).
Area Coverage Differences
The small area essentially covers most/all of Hiroshima city via trams and bus, as well as Kure and Miyajima. Yes, this pass will cover the ferry to Miyajima. (Note that there are two companies providing ferries to Miyajima: Miyajima Matsudai Kisen, and JR West Miyajima Ferry. The pass says you can use either company; when I used this pass in fall 2016, the person at the gate of JR West asked me to take the Matsudai Kisen ferry. I'm not sure if the information on the official site is mistaken or the person at the JR West gate just hadn't seen the pass before. The person at the Matsudai Kisen ferry waved me through without any issues, though.)
I didn't go to Kure, but I used this pass to explore Hiroshima for two days using the streetcar and bus, and then Miyajima on the third day. Note that this train does not cover JR lines, only city-run trams (and buses). The trams will take you to pretty much all of the main tourist spots.
The wide area pass covers significantly more ground, allowing you to travel via express bus to some other cities, in addition to everything covered by the small area pass. If you're in Hiroshima for 5+ days and want to explore beyond the city, this may be a great option if you're interested in any of the cities shown on the map.
Both passes also come with a little booklet that show a map of the covered area, as well as sample itineraries and some restaurant coupons. The passes themselves is shaped like a slim card, and will have the validity date stamped on it the first day you use it. It also features instructions on the back on how to ride a streetcar and bus, which is handy if you're nervous about it!
Airport Limousine Bus Route Add-On + 2 More Days
Note that there are buses available to/from the airport (from/to Hiroshima Station or the bus terminal) for 1340 yen one-way. If you're interested in timetables for that, they're available on the Hiroshima Airport website. I would assume that with the limousine bus add-on, you would be able to do a round-trip from the city to the airport, in addition to having two extra days to use the pass. However, if you're not planning on flying out just four days after flying in, this add-on likely isn't that helpful for you. Even if you're in Hiroshima for 5 or more full days, it may be a better idea just to buy another pass without the airport limousine add-on; for example, you can buy the small area pass, use it for days 1-3 to explore Hiroshima/Kure/Miyajima, and then buy a wide area pass for days 4-6 to go out of the city. Those two passes plus a one-way ticket for an airport bus would come to about 5500 yen, rather than 6000 yen, plus you get an extra day to use the pass.
If you would like to travel a bit outside Hiroshima but find trains a bit pricey, even with a train pass, the wide area pass may be a helpful option. For just an extra 2000 yen, you can spend one day in Hiroshima, one day in Miyajima, and then take a day trip out to any of the cities shown on the wide area map. (With enough planning, I do think you can see most of the main tourist spots within Hiroshima in a day.) As a price comparison, a round trip by bus from Hiroshima to Onomichi (~90 minutes each way) would already be about 3000 yen. The only caveat is that this pass doesn't cover transportation within that city, but most of these places would likely be walkable anyway. Or, as I described above, if you have time, you can use the small area pass to explore the the local area for three days, and then spend another three days just doing day trips out of the city. While I haven't used express buses in Hiroshima, the ones I've taken in other places in Japan have all been comfortable coach buses, so they're very comfortable to ride. They're a great alternative to trains for those on a budget!
I purchased this pass at Hiroshima Airport, but it can also be purchased at Hiroshima Station.