Insurance and hedging both reduce your exposure to financial risk, but they do so in different ways. Insurance typically involves paying someone else to bear risk, while hedging involves making an investment that offsets risk.
Insurance Shifts Risk
Buying an insurance policy that protects your home against fire does not guarantee that your home won't burn down. Having auto insurance doesn't mean you won't crash your car, and life insurance won't keep you from dying. What insurance does is shift potential financial losses from you to someone else. If your house burns down or your car gets totaled, you don't have to pay to replace it because the insurance company does.
Hedging Offsets Risk
Hedging reduces uncertainty, which is really just another word for risk. For a simple example, say you do a lot of business with Europe, and you've discover that you lose money if the exchange rate rises above $1.50 per euro. So you buy a series of options contracts that give you the right to buy euros for, say, $1.40 per euro. Those options offset your risk from rising exchange rates. If the rate never rises about $1.40, then you just let the options expire. But if the rate tops $1.40, then you've locked in an exchange rate that offsets the increase and protects your profit. The options, therefore, are hedges.
Both insurance and hedges cost money -- premiums in the case of insurance, and the price of the options in the hedging example. But those costs are less than the losses you're protecting yourself against. That's why the expense is considered worthwhile.