Last updated for Star Citizen 2.6.3
Insurance in Star Citizen is just like insurance in real life. If a possession of yours which is covered by insurance is either stolen, damaged or destroyed, you'll be compensated.
You can purchase insurance in Star Citizen for your ships. This means that if your ship gets stolen, damaged or destroyed you'll be issued a replacement free of charge.
Insurance has not yet been fully implemented into Star Citizen. There is no way to purchase ship insurance, and there's no need for it either. If you ship gets destroyed you'll be sure to get it back within a few minutes.
If your Star Citizen ship is destroyed in-game, whether it be from another player or from your bad piloting skills, you'll always get it back. This will change in the near future unless your ship has LTI (life time insurance)
Lifetime insurance is only available for a ship if you purchased it with real money whilst it was still in concept. This means that you purchased it before it was made available in-game.
You'll be required to purchase insurance for each individual ship you own. There will be many different insurance dealers, some for UEE ships, some for Alien ships and some for stolen ships.
Ship insurance will be system-wide. This means if you leave the system, your insurance won't cover you. The price of insurance will depend on how dangerous the system you're in is. CIG has stated that insurance won't cost too much and but it will be something that you'll need to look out for.
If you've got a record of churning through ship fast, then insurance companies will raise their prices accordingly.
When insurance has been fully implemented into the game, anything that gets stolen, damaged or destroyed which you do not have insurance for will not be compensated for.
For example, if your ship gets destroyed in a fight with pirates, you'll have to purchase another one. If you don't have enough credits you'll have to work as a member of a crew on a large vessel until you've got enough cash to purchase a ship of your own.
Yes, it will be possible however you'll need to find an insurance company who is willing to do so. You'll be paying a high price and there's no guarantee that they won't rip you off.