Multi signature wallets allow users to maintain direct control over their bitcoins while also removing some of the security burden from them. In the event that one of their private keys is lost or stolen, it’s no longer a catastrophe. The concept in m-of-n signature schemes is fairly simple, at least at an abstract level–in order to complete a transaction, more than one private key (m) is needed out of a total number generated (n). In a 2-of-3 scenario, you would need two out of a total of three keys to withdraw money, but the process for deposits is the same as it would be for a standard address. You can then approach distributing and storing the keys in various ways. You could hold one key, you could give one (the backup) to a trusted friend or relative, or even store it yourself in a different location from the “main” key, and the third key would be held by yet another party, such as the company offering the service. BitGo is at the forefront of implementing multisig addresses, so I recommend you check them out.