Home Warranties are different from Homeowners Insurance. Home insurance simply covers the structure in case of a catastrophe. A Home Warranty covers the repair or replacement of many major home system components and appliance that typically break down over time due to normal wear and tear. It covers things from garbage disposals and cook tops all the way to water heaters and your AC unit. If a home system or appliance breaks down then you call the home warranty company. They will get in touch with the service provided who will then contact you to schedule an appointment to come and fix the broken item. Depending upon your agreement contract, if they can't fix it then they will pay to have it replaced. You will usually be charged a "trade service fee" for them to come out to your home. However, this is usually less than $100.
It's important that you know exactly what is covered in you home warranty. And don't assume that all home warranties are the same. Make sure you do your research. For instance, if your AC is broken, many companies will charge you for new freon in addition to your trade service fee.
Like closing costs, a home warranty is something that can be negotiated in the purchase of your home. In fact, there is already a spot in the Real Estate Purchase Contract the spells out if one will be included and if it will be paid for by the buyer or seller. I recommend including one in the purchase of your home (no matter if you or the sellers pay for it) for at least the first year. It would really stink to move into your new home and have the fridge break 2 days later; after you already spent what money you had left on new furnishings.