The easiest answer to your question is one word: value. Stock and Mutual insurance companies are the two primary types of insurers on the market. Stock and mutual insurance types define how the company is owned, and that difference can mean a great deal to you as a consumer. In one case, the company owned by investors, while the other one indicates that the policyholders are the actual company owners.
For consumers, buying into a mutual insurance company will usually yield the lowest rates. The reason is that a mutual insurance company is, at least in part, owned by the policyholders. The company is called a mutual company because it is owned mutually, or together, by the participants in the company. Procedures and decisions for the company are typically made by an elected or appointed board of directors who act on behalf of the policyholders as a whole.
A stock insurance company is traded, either on the open market or privately among a specific group of investors. Stock companies tend to charge slightly higher rates, aimed at earning a profit for the investors. In a stock insurance company, decisions and procedures are made by a board of directors who are either major stockholders or appointed to the position by major stockholders.
The easiest way to think of it is that a mutual insurance company belongs to the consumers who purchase policies while a stock insurer is owned by people who have invested cash directly into the company. Both types of companies issue the same types of policies are issued by both types of companies and the underlying difference between the two may never even have an effect on the individual policy owner.