The human interest in the question how organisms work - how they are and stay alive - goes way back. So, it is only natural for us to ask the same question.
Let’s take a cat as our example. A cat is a living being because it possesses the characteristics of life: It grows, it conducts metabolism (it breathes, it eats, it excretes certain substances), it moves, it is able to produce offspring, and it perceives stimuli from its environment and is responsive to them.
Soon, it was discovered that certain organs are responsible for the performance of these characteristics of life.
Breathing is conducted by the lungs, muscles create a cat’s movements, the kidneys produce the urine which gets excreted, etc.
When people started examining these organs more closely, they realized that they can be subdivided into certain subunits. These subunits – called tissues - each contribute to the overall function of the organ with a specific task. In the kidneys, for example, there are tissues responsible for filtering waste products from the blood. Others reabsorb water from the forming urine.
Later, it was discovered that these tissues themselves consist of subunits which we call cells. Just like our cat, cells exhibit the characteristics of life, too: They grow. They conduct metabolism. They move (with some constraints). They can reproduce, and they are receptive to stimuli from their environment.
Although cells consist of components themselves (the cell organelles), they are the smallest “unit of life” because, in contrast, cell organelles generally don’t display the characteristics of life.
To sum it all up, the cells of a cat are alive, and they have certain functions. Together with similar cells with similar functions, they form complexes, called tissues. These tissues cooperate with other tissues working on different tasks in order to achieve the overall purpose of the organ they belong to. And these organs and their specific functions achieve that the cat is alive and that it can entertain us with its shenanigans.