A Unit Linked Insurance Plan is a type of life insurance that invests part of your premium in the market. When you pay your premium, the insurer splits it into two parts:
Insurance Part: This pays for your life cover so your family is protected if something happens to you.
Investment Part: The rest is invested in funds you choose from equity funds to debt funds or balanced funds.
Each fund is divided into units and the price of each unit is called the Net Asset Value. As the market does well or poorly your fund value goes up or down. When your policy matures or you surrender it you get the payout based on how your fund performed.
Unlike a term plan, which only pays out if you die, a Unit Linked Insurance Plan gives you value whether you die or survive the policy term. That is why it is like "insurance that invests" than "insurance that waits."