Options can be used in three major ways:
- Buying them for speculation (long calls or long puts)
- Selling them for income (short puts, covered calls)
- Using them to hedge other positions, aka insurance (put protected stock)
Note that there is some overlap in these three categories. For example, spreads would qualify as income oriented and hedging.
To keep it simple, I'm going to consider the hedging of a long equity position.
Regarding use as insurance, one could buy a long put (generally at or out-of-the-money) to protect long stock. The cost of the insurance is the premium and the deductible is the distance from the stock's current price down to the strike price. This is analogous to an insurance policy on your car, house, etc.
However, options are not that simple. If you're willing to cap the upside, a low/no cost long stock collar can be employed (sell OTM call to fund the cost of the put). Now, you only face the deductible.
Due to the nature of options, in some circumstances, their payoff can increase. For example, the underlying drops and implied volatility increases, further increasing the value of the a put.
In addition, because of the ability to roll options, you can capitalize on their price appreciation, booking option gains while maintaining 'insurance' protection.
Overall, I would say that it is not true that "the primary purpose of options to provide insurance against changes in the stock's underlying value." For the large part, they have become tools of speculators, betting on short term moves.