Interesting that this came up in my search for Hawaii here, as I've just started listening to the podcasts and searching the site. "First post!" I've just picked up a house on the Big Island. I think I've learned a bit about the basics of the market out there. Granted, I'm toying with the notion of investing, but not serious about it yet.
Anyway. All the islands are great. Kauai is probably my favorite. While "deals" can be found on all of the islands from what I can see, all but the Big Island, Molokai, and remote areas of Maui your'e going to pay unless you get something that is a flip. ...and even the things "worth buying" as "livable" out there you'd be surprised by how bad they can be left sometimes (the stuff that flies out there would never fly on the mainland, but hey, it's paradise, right?).
The Big Island is an interesting place. You can actually find investments out there, but the problem you have is that whole market is in a pretty good upswing, and it's going pretty fast. I started entertaining the notion of buying my "death home" out there last Feb. when I first visiting to the house I closed on earlier this month, and in that time, the avg. price of homes even on the BI jumped about $50k. Even as I was closing seems like values were creeping up (I actually ended up appraising higher than acquired price...I could even wholesale to the tune of $12-20k if I wanted, but I found a place that met all 3 of my criteria for getting out there someday, so I'll likely keep it).
Also, Leasehold, yes, as has already been pointed out, your buying a house only on a property that has a lease with a term. I was warned by my realtor to avoid them because they do come with quite a few hassles. It is NOT true that most lands are Leasehold. But depending where you are and on what island, you will find there are quite a few.
A bigger problem you end up having (which is an issue in large swaths of Maui from what I was seeing) is there are lands that have a nativity requirement. If you are not a percentage native Hawaiian or married to a Hawaiian, you cannot be an owner of a native restricted piece of land.
Then there are the standard, non-restricted, "Fee Simple" properties. Fee Simple is a standard sale. They also have all of the standard REOs, etc., and that's something you'd want to look for in the listing of a whatever you're getting, you may or may not want that depending on what you're trying to do (I was trying to close on the house I want to occupy in the land I wish to pass away in, and do so before I was priced out of the market, so I was looking for affordable housing not encumbered by bank skittishness, meaning standard owner, non-foreclosure sales).
Hope that helped at all. It's been an "interesting" process working out there. Oh, also, as I've been made aware (and I don't think it's b.s., but I guess someone may know better than I), you are strongly encouraged to use Hawaii lenders/brokers, because there is apparently a lot of weirdness in how they handle things. You apparently CAN use mainland lenders, but I've heard it causes hiccups in the process. I found a pretty good broker that dealt with a lot of things and even smacked around the title company when they were going to do something stupid and cost me more money.