Islamic insurance is permissible. As for conventional insurance, it is a new kind of financial contract not known in the history of fiqh. Muslim scholars have different opinions regarding it.
Dr. Monzer Kahf, a prominent economist and counsellor, states: You know its authenticity from trusting the truthfulness of the company that provides it, the supervisory authority that allows it to make such a claim [of being Islamic], and the Shari`ah advisory board of the company. If you trust all these, then the claim is correct; if you don’t, the claim may not be correct.
In brief, the difference is: Islamic insurance is provided on cooperative basis, and its premium is not a price of covering the risk but a membership in that cooperation that provides these services. Conventional insurance is based on exchange between two parties, and the premium is a price of covering the risk.