The reason most people buy Term Life Insurance is for peace of mind. Period.  Term provides a very affordable way to ensure a lump sum will be paid to your beneficiary upon your death.  The ensures your loved ones will continue to pay the bills and the mortgage, pay for your funeral and have financial stability.  

Think of Term Insurance as renting a policy.  You purchase a certain amount of coverage for a certain amount of years.   If you die within the time when the policy is active, your beneficiary receives the face amount of the policy.  Premiums vary but are usually level for the duration of the policy.  Some policies also have return of premium riders if you outlive the policy.

The reason most people buy Universal Life Insurance if for the flexibility and cash value accumulation.  This policy can be used as a death benefit policy as well as a savings account with a much higher average interest rate.  This policy is also permanent so once you have it .. its forever.

Think of Universal Life Insurance as buying a policy.  This is a permanent policy for the duration of your life.  There is flexibility in premium payments and also cash value accumulation in the policy.  Premiums are paid monthly.