Others have really answered a lot of your questions about termites and I am sure that you can do some research on google to get more specific information, but here is a little bit more:
Termites are attracted to wood. They eat it. They build colonies and start munching on wood. Here in Texas, a lot of our houses are built on slabs, so I am going to make the assumption that your house is built on a slab as well. Often, what people do is put a lot of landscaping around the house and they cover the slab with mulch. The termites can then enter the home and get to the wood framing of the house. Most often, this occurs at the perimeter of the home and the termites start munching on the framing. The damage that happens is that the framing structures and the wood that runs along the bottom of the framing (the piece on the slab) gets eaten and it loses its structural integrity. In very very very severe cases, those walls can collapse or at least not support anything (ie if termites are in your garage wall, you may not notice anything on the wall itself, but when you try to attach a shelf in the garage, the screw cannot bite into the wood because the wood is so severely damaged).
As others have said, termites happen and these people got it treated. If they had a termite plan where they were getting inspections annually, they may have just caught the beginnings of a colony and then did the abatement and wiped out the colony (no damage). But, if they weren't doing inspections, they may have had extensive termites and had to do more abatement. Again, this may mean that there was no damage. But, if there is extensive damage (it behooves you to get an inspection done and get a quote on the cost of what it will take to repair the damage), then you have options about how to deal with the damage. If you do get a quote, here are some of your options:
1. One option is to say, it's going to take $5000.00 to repair the house, we would like you to reduce the cost of the house by $5000.00.
2. It's going to take $5000.00 to repair the house, we would like you to repair the house before we close (write it into the contract).
3. It's going to cost $5000.00 to repair the house, please put this money into escrow so we can use it to repair the house (this would again be part of the contract. At closing, the money would go into escrow and you could use it to repair the house).
If there is extensive damage and you decide to buy the house, but not repair it (because it may be pretty minor), then you will face this issue when you go to sell the house - you will have to do something about the damage.
Now, if there really is not much damage, you need to take appropriate actions to maintain the house over the years. Get termite inspections, but also take landscaping that is high up on the house (piled mulch) and rake it back. You should never cover the slab with mulch. You also should not let bushes that are surrounding the house grow so thick that they touch the house. You should keep these cut back. If there are any railroad ties within 3-4 of the house, you should remove those.
I really don't think you can make your decision until you get a report back from the termite inspector. And, be prepared to know that the termite inspector is NOT an expert on estimating what the cost of the repairs will be. Unless the guy also does construction, I would definitely get a contractor to look at the damage and give an estimate of what it takes to make the repairs.
Once you do buy the house, you can buy a termite inspection plan. I'm not 100% sure what the costs are, but it includes an annual inspection and then a spray treatment if they find termites. You don't have to go with the "name brand" termite people. I find that just for maintenance, the name brand people are pretty expensive. Lots of local bug companies offer termite bonds.
Good luck,
L.