Term life insurance expires, so once your coverage time ends, your policy ends as well. This means that you would then need to re-apply for a new policy (which may be harder and more expensive at that time) if you still needed coverage.
Whole life insurance never expires. So you can keep the policy as long as you need without the price increasing, despite aging or having any health issues arise. This can be comforting for some people who worry about their health deteriorating.
The cost of whole life insurance is one of the biggest drawbacks to purchasing this type of policy. As noted, it is much more expensive than term life insurance because of the added cash-value component of the policy.