As a property owner, if someone gets hurt on your property, they may be able to sue you for their medical costs and their pain and suffering. There are a lot of things that go into whether or not they can sue you.
One of the big things that goes into whether or not you can be sued by someone who got injured on your property is what their status was. The basic statuses are invitee, licensee, or trespasser. An invitee is someone who has been invited to come onto or into your property, such as if you were operating a business and they were your customer or client. In the case of an invitee, it is assumed that you have taken all reasonable steps to make sure that the invitee will be safe. A licensee is someone who comes onto your property, with your permission, on their own business or as a guest you have invited socially. For example, a meter reader or postal worker would be a licensee. A trespasser is someone who has no permission to come on your property at all and has not been invited. When it comes to a licensee and trespasser, there is nothing that promises that all reasonable care for their safety was taken.
Your state may require you to place warnings up if there is something that could cause injury to a licensee or even a trespasser. The warnings are about something that you have created and that you know may cause someone to be injured or worse because of that thing. It also has to be something that you actively maintain. For example, if you have a dog that has a history of biting, you would need to post signs that would state that people should beware of your dog. Likewise, if you have a rickety bridge on your property that you know is there and you have chosen to not repair it because you like it the way that it is, you may be required to post a warning on either side of the bridge warning trespassers that the bridge is in poor conditions and that there is a risk they could get injured.
If someone has been injured on your property and is suing or threatening to sue, you should immediately talk to a lawyer who specializes in personal injury law. They will be able to defend you and help to get rid of any lawsuit.