There must be insurable interest between you and the person you want to insure for life insurance in order for you to be eligible to buy life insurance on another person.
For instance, there is insurable interest between spouses, parents and their children, siblings, relatives, and business partners, among others.
And, for example, since you are the child of your parent, you may be eligible to buy life insurance on your parent. However, you may need your parent's permission, signature on the application for life insurance, and you parent may need to answer some health questions, and/or take a physical exam to find out if he/she qualifies for life insurance.
Here's how you can learn more about insurable interest.