An ATA Carnet is the equivalent of a passport for your equipment. It is not insurance, you need to have that too to protect yourself in the event of a loss of equipment.
When you have one created, they will charge you for a bond for the amount of equipment that you are traveling with. You will need to manifest each case when you fill out the paper work. ATA will then send you a folder with all of the paperwork. Stop at customs, show them your carnet and equipment on the way out of a country and on the way in. They will stamp your forms and allow the equipment to pass.
Without a carnet you are risking your gear being held at customs until a local customs broker can give you a bond and get it signed and approved. This could take an hour or days. We had a shooting crew on an event in Bahamas that thought they would just tip their way through customs and baggage claim. If it weren't for the hotel we were at, their gear would have not made it into the country at all. It cost about 3,000 US to get it bonded and out of customs since they didn't have the carnet.
Carnets are pretty cheap to obtain with a bond.
If you have something lost or stolen make sure you get a police report. Customs will want that as proof you didn't sell the gear. Even if you do end up selling something to a local, prepare a bill of sale and be prepared to pay the duty on leaving the country.
This is who we use http://www.atacarnet.com/what-carnet?gclid=COfBipCqobICFQKCnQodAjEA_A
Great people, fast and always ready to answer a question.